Does the Immirzi Parameter Determine Black Hole Entropy in Loop Quantum Gravity?

[Physics Monkey]

I would like to discuss a puzzle I'm wondering about in loopy approaches to quantum gravity.

The puzzle is roughly as follows:
The Immirzi parameter (IP) is a strange constant that appears in loopy approaches. Calculations of black hole entropy in loopy approaches seem to need to fix the IP to be a particular value to agree with semi-classical entropy calculations. On the other hand, http://arxiv.org/abs/0809.2280 suggests that the IP plays little role in establishing the semi-classical limit of certain spin foam models. So what gives? Have I misunderstood something elementary? Will we find that the IP is given by the black hole value via other means? If not, what do the loopy approaches describe when the IP is not tuned to the black hole value? It almost seems impossible to have a semi-classical limit of GR for all IP, but only be able to reproduce the semi-classical black entropy for a particular IP.

Please let's keep the discussion to the science as much as possible. Thanks!

 

[atyy]

I don't know. I wonder if it is true for all the major spin foam models (Barrett-Crane, EPRL, FK). Also, I don't know how exactly each of these can be joined to the canonical spin network framework that Krasnov was presumably using.

 

[marcus]

I would like to discuss a puzzle I'm wondering about in loopy approaches to quantum gravity.

The puzzle is roughly as follows:
The Immirzi parameter (IP) is a strange constant that appears in loopy approaches. Calculations of black hole entropy in loopy approaches seem to need to fix the IP to be a particular value to agree with semi-classical entropy calculations. On the other hand, http://arxiv.org/abs/0809.2280 suggests that the IP plays little role in establishing the semi-classical limit of certain spin foam models. So what gives? Have I misunderstood something elementary? Will we find that the IP is given by the black hole value via other means? If not, what do the loopy approaches describe when the IP is not tuned to the black hole value? It almost seems impossible to have a semi-classical limit of GR for all IP, but only be able to reproduce the semi-classical black entropy for a particular IP.

Please let's keep the discussion to the science as much as possible. Thanks!

I'm glad to see you had the time to read that LQG paper! Since you have some time to devote to LQG, it would be efficient (for our discussion) if you would get the one "official" version under your belt by reading
http://arxiv.org/abs/1102.3660.
We may waste a lot of time if we jump around among different versions, as they were seen 3 years ago.
Things have settled down considerably since 2008!

The Immirzi plays an extensive role in defining coherent states and in studying the semi-classical limit of the current theory. As of today.
See page "Section V: Extracting Physics" starting on page 14 of the standard paper.
It will have a section on defining coherent states, and in particular the socalled "holomorphic" coherent states with SL(2,C) labels.

Page 8 gives a sketch of the mathematical role played by this parameter. The symbol used is gamma, see equations 42-47, 49 and 50. Basically it defines a class of SL(2,C) reps and a map from SU(2) to SL(2,C). Then gamma shows up in equation 57 on page 9.
This is the definition of the theory (it is defined by specifying transition amplitudes).

There is an alternative compact definition given in equation 60, where gamma also appears.
=====================

There is no inconsistency that I can see. Gamma is essential in defining the transition amplitudes that define the official version of the theory. And it is also essential in any discussion of the semiclassical limit of the present official version of the theory and in any other aspect of "extracting physics".

You might like to read the "extracting physics" section. It covers a half-dozen topics and is only about 6 pages long.

We shouldn't always be jumping around amongst different people's versions many of which have been superseded or effectively abandoned. More efficient to stick with the one version.

 

[atyy]

marcus, which is the paper where EPRL is related to the old LQG spin network states?

That's the only connection between the spin foams and old LQG, or are there others?

 

[marcus]

Atyy, I'm not sure what you mean by "EPRL".

There is one Loop Gravity theory, now. That is what the Zako school meant and the way the Zurich conference is coming together. It makes predictions and (besides completing, elaborating) the job is to test it.

In the defining paper 1102.3660 he gives three equations and then says "This defines the theory."

In folk vernacular, this nails the coonskin to the wall.

Every question we ask about Loop Gravity from now on, every conclusion we draw, refers to 1102.3660.

I can't be sure what you mean by EPRL because unless you specify that term might refers to some 2007 papers, or maybe some 2008 papers etc etc.

The first time I ever saw the present version of Loop was in March-April 2010 and it is RADICALLY different. It does not use a spacetime manifold! And the first reasonably complete presentation is 1102.3660---what I am calling the "offiicial" version.

Drastically redefining like this was a bold move, it might have misfired, but it looks like the Marseille group is carrying it off.
=================================

So what kind of "connection" are you looking for? The explicit mathematical connection is explained in 1102.3660 and is based on the Peter-Weyl theorem.
Remember we are in H-sub-Gamma, a graph Hilberspace.
All the possible spin networks are just the possible labelings of that graph Gamma, with irreducible representations.
Courtesy the Peter-Weyl theorem these form an orthonormal basis for the Hilbertspace.
It is in the paper---the connection with the usual idea of spin network---if you look for it.

The relevant section of what is now our defining LQG paper is on page 5. It is the section headed "Spin network basis."

There really is no need for a "connection", is there? They are the same familiar spin-labeled graphs as before.

It's rather elegant that they arise in a GFT-like setting where you do not have a spacetime manifold! You have a Hilberspace of integrable functions on a group manifold, and the same old spin networks arise as an orthnormal basis of that vectorspace!

 

[atyy]

Ok, so basically it looks like the Immirzi parameter remains in the EPRL asymptotic analysis, but apparently not in FK. EPRL does connect to the old LQG formalism, but FK? OTOH, FK overlaps with EPRL for some values of Immirzi, so what is going on?

BTW, EPRL is http://arxiv.org/abs/0711.0146 .

 

[marcus]

Ok, so basically it looks like the Immirzi parameter remains in the EPRL asymptotic analysis, but apparently not in FK. EPRL does connect to the old LQG formalism, but FK? OTOH, FK overlaps with EPRL for some values of Immirzi, so what is going on?

I am not sure what you mean either by EPRL or by FK. There was a lot of confusion in 2007-2008 and when the dust settled there was something that didn't really look like either.

What do you mean by "FK"? Has it been shown to be Lorentz invariant? Does it have fermions? Does it have general spinfoams with more than 5-valent vertices, not necessarily dual to some triangulation? Has it been shown to give quantum cosmology with a quantum corrected Friedmann equation? Does it have a comprehensive entry-level presentation? Does it have a presentation in terms of Feynman rules?
Maybe it is not fully developed.
I didn't see any discussion of it lately, like at the Zako school.
So why are you talking about "FK"? Maybe it was subsumed in today's theory.

Let's refer to actual 2010 and 2011 papers.

If someone wants to read about the HISTORY there is a very nice history paper
http://arxiv.org/abs/1012.4707
"Loop quantum gravity: the first twenty five years"
It covers the past 25 years and it will certainly describe the various attempts.

 

[atyy]

FK: http://arxiv.org/abs/0708.1595
EPRL: http://arxiv.org/abs/0711.0146

 

[marcus]

FK: http://arxiv.org/abs/0708.1595
EPRL: http://arxiv.org/abs/0711.0146

Then let's avoid mentioning either of those papers. Today's Loop Gravity is very different.
I think it is pointless to argue now about which group had the biggest influence on todays LQG.
That is history.

We are on a completely new footing now. The presentation is clearer and better than it was back at the 2007 origins. Let's avoid free-floating references to stuff before 2010 and bothering with these acronyms.
Probably all these pre-2010 papers contributed important insights. These useful contributions and historical points would be brought out in footnotes and references in the current papers.

If you are really interested in the history, if the 2007 developments have a special fascination for you, maybe we should have a special history thread and try to go through that 1012.4707 paper "The First 25 Years."

Right now I see that as a low priority distraction. I want to understand the physics, not the history, and the physics is in 1102.3660.

 

[atyy]

Then let's avoid mentioning either of those papers. Today's Loop Gravity is very different.
I think it is pointless to argue now about which group had the biggest influence on todays LQG.
That is history.

We are on a completely new footing now. The presentation is clearer and better than it was back at the 2007 origins. Let's avoid free-floating references to stuff before 2010 and bothering with these acronyms.
Probably all these pre-2010 papers contributed important insights. These useful contributions and historical points would be brought out in footnotes and references in the current papers.

If you are really interested in the history, if the 2007 developments have a special fascination for you, maybe we should have a special history thread and try to go through that 1012.4707 paper "The First 25 Years."

Right now I see that as a low priority distraction. I want to understand the physics, not the history, and the physics is in 1102.3660.

Well, I guess LQG has only one paper. What a small field.

 

[marcus]

Well, I guess LQG has only one paper. What a small field.

Actually something over 150 LQG papers in 2010-2011.
I've suggested we use 2010 and 2011 papers in our discussion. There are loads and loads. More than we can keep track of really
I'd narrow it down further than that.

It's distracting to have quotations picked out of context from earlier papers which may have contributed greatly in their day but don't contain the most recent understanding.
It really helps to try to stay abreast of the field.

Just for fun, I did a check with Inspire:
http://inspirebeta.net/search?ln=en...2y=2011&sf=&so=a&rm=citation&rg=50&sc=0&of=hb

It finds 128 Loop gravity/cosmology papers in 2010 and 30 so far in 2011, so 158 in all.

 

[atyy]

Actually something over 150 LQG papers in 2010-2011.
I've suggested we use 2010 and 2011 papers in our discussion. There are loads and loads. More than we can keep track of really
I'd narrow it down further than that.

It's distracting to have quotations picked out of context from earlier papers which may have contributed greatly in their day but don't contain the most recent understanding.
It really helps to try to stay abreast of the field.

Just for fun, I did a check with Inspire:
http://inspirebeta.net/search?ln=en...2y=2011&sf=&so=a&rm=citation&rg=50&sc=0&of=hb

It finds 128 Loop gravity/cosmology papers in 2010 and 30 so far in 2011, so 158 in all.

You must subtract all papers that deal with EPRL and FK.

 

[fzero]

Actually something over 150 LQG papers in 2010.
I've suggested we use 2010 and 2011 papers in our discussion. There are loads and loads. More than we can keep track of really
I'd narrow it down further than that.

It's distracting to have quotations picked out of context from earlier papers which may have contributed greatly in their day but don't contain the most recent understanding.
It really helps to try to stay abreast of the field.

I have to say that, for the last 10 yrs it's been extremely difficult to figure out what LQG is doing because everyone seems to have their own pet theory. At any given time, there were several spinfoam models, CDT, BF theories. Some papers are about semiclassical physics, like the one PM cited in the OP, others are not. Some methods are purely topological and therefore don't seem to have any propagating degrees of freedom. It's difficult for even a theoretical physicist to figure out that any particular approach is worth learning.

Perhaps at some point we can try to figure what old results apply in the new framework. Does the BH entropy calculation change, LQC and the bounce, etc?

Anyway, to try to say something on topic, I believe in the paper cited in the OP, they claim that the Immrizi parameter drops out because their analysis is semiclassical and the classical physics should not depend on the parameter. There were also a couple of papers that came out this month on semiclassical approaches, one on BF and the other on black holes (both listed in the running thread that marcus keeps), that also derive results that seem to be independent of the Immrizi parameter.

 

[atyy]

Basically, I disagree with marcus's reading of the current literature. My reading is as follows.

1. The key models are in fact EPRL http://arxiv.org/abs/0711.0146 and FK http://arxiv.org/abs/0708.1595 .

2. The semiclassical limit of a component of the EPRL and FK path integrals appear to go as ~ exp(iS_Regge) http://arxiv.org/abs/0902.1170 , http://arxiv.org/abs/0907.2440 , http://arxiv.org/abs/0809.2280 .

3a. As Physics Monkey brought up, the Conrady and Freidel paper on the semiclassical limit of FK seems to get a term that is independent of the Immirzi parameter.

3b. The Barrett et al papers on the semiclassical limit of EPRL seems to me to contain the Immirzi parameter.

3c. I don't know whether the difference between the Conrady and Freidel results is because they are calculating the same thing in different models, or slightly different things in different models.

3d. I believe the EPRL and FK models overlap for some range of Immirzi parameter, so they are not entirely different models.

4. I haven't followed the LQG black hole literature, but the key original paper seems to be http://arxiv.org/abs/gr-qc/9710007 , with more recent papers being http://arxiv.org/abs/0905.3168 , http://arxiv.org/abs/0905.4916 , http://arxiv.org/abs/0911.3553 , http://arxiv.org/abs/1101.3660

 

[marcus]

I have to say that, for the last 10 yrs it's been extremely difficult to figure out what LQG is doing because everyone seems to have their own pet theory. At any given time, there were several spinfoam models,

... what old results apply in the new framework. Does the BH entropy calculation change, LQC and the bounce, etc?
...

The 22-pager I mentioned discusses what results apply in the new framework.
Much of the work in the past year seems to have been devoted to making sure.
There is a paper by Battisti and Marciano about the bounce.

You should be happier now that there is effectively one "official" version.
It is the Marseille group's version but it draws on everybody's work.
And it is formulated unambiguously as a theory, not as an "approach" or a theory-in-the-making.

It's a bold move, we'll see how it goes. There are risks in going from an "approach" or a bunch of tentative formulations to an actual theory.

For anyone who wants to follow the field, it has become a lot simpler to do this since
1102.3660 appeared and got recognized community approval by being featured at the Zakopane school.
Another key sign is the increased exchange of postdocs between Penn State and Marseille.
Ashtekar just took in Magliaro and Perini (who helped formulate the present version)
and the exchange is both ways.

We still don't know if the field will now cohere around this version. But what I see happening says yes, it will go. And in any case there is a theory which phenom'sts can test
====================

I'm glad to find someone here who has been watching LQG for 10 years, as I gather you have from what you say.
I only started watching the field in 2003, not quite as long as you.

 

[atyy]

The FKand EPRL models are the same for Immirzi parameter <1 (which is the region needed for the Krasnov calculation to match the Bekenstein-Hawking result). Conrady and Freidel http://arxiv.org/abs/0809.2280 get a semiclassical limit without IP dependence , while Barrett et al http://arxiv.org/abs/0907.2440 get terms with and without IP dependence depending on their boundary states (Eq 53, 54). I wonder if Conrady and Freidel in fact assumed boundary states more like those in Barrett et al's Eq 54.

 

[Physics Monkey]

It's distracting to have quotations picked out of context from earlier papers which may have contributed greatly in their day but don't contain the most recent understanding.
It really helps to try to stay abreast of the field.

This is unwise in my opinion. I don't know any practicing scientists who restrict themselves to only the most recent work, especially not short review articles. For example, there is all kinds of juicy information in older works that get absorbed into the collective consciousness and stop being repeated. I would prefer it if people contributing to this thread felt free to bring in any paper they liked if it contains useful information about the physics in question.

 

[Physics Monkey]

Anyway, to try to say something on topic, I believe in the paper cited in the OP, they claim that the Immrizi parameter drops out because their analysis is semiclassical and the classical physics should not depend on the parameter. There were also a couple of papers that came out this month on semiclassical approaches, one on BF and the other on black holes (both listed in the running thread that marcus keeps), that also derive results that seem to be independent of the Immrizi parameter.

This is interesting, the claim would be that new black hole entropy calculations don't depend on the Immirzi parameter? Or perhaps we should think of the IP as being absorbed into Newton's constant in the semiclassical limit? I shall have to try and track down the paper you mentioned, unless you have a reference off the top of your head.

 

[Physics Monkey]

The FKand EPRL models are the same for Immirzi parameter <1 (which is the region needed for the Krasnov calculation to match the Bekenstein-Hawking result). Conrady and Freidel http://arxiv.org/abs/0809.2280 get a semiclassical limit without IP dependence , while Barrett et al http://arxiv.org/abs/0907.2440 get terms with and without IP dependence depending on their boundary states (Eq 53, 54). I wonder if Conrady and Freidel in fact assumed boundary states more like those in Barrett et al's Eq 54.

Interesting, so you're suggesting that perhaps Conrady and Freidel assume something too specialized to see IP dependence?

Perhaps it would be useful to understand to what extent the Planck length, Newton's constant, and the IP are separate entities. They appear multiplying each other in a specific way in the black hole computations. The usual equation is \ell_P^2 = \gamma G_N neglecting some constants (there is typo in one of Rovelli's lectures on this point). Nevertheless, in semi-classical GR what appears directly is G_N while what appears directly in LQG seems to be \ell_P^2. So I continue to feel that unless I'm making some trivial mistake, then somehow the semiclassicl limit should only work if the IP has a specific value. Otherwise we can compute black hole entropy in two different ways and get two different answers.

 

[Physics Monkey]

I'm glad to see you had the time to read that LQG paper! Since you have some time to devote to LQG, it would be efficient (for our discussion) if you would get the one "official" version under your belt by reading
http://arxiv.org/abs/1102.3660.
We may waste a lot of time if we jump around among different versions, as they were seen 3 years ago.
Things have settled down considerably since 2008!

The Immirzi plays an extensive role in defining coherent states and in studying the semi-classical limit of the current theory. As of today.
See page "Section V: Extracting Physics" starting on page 14 of the standard paper.
It will have a section on defining coherent states, and in particular the socalled "holomorphic" coherent states with SL(2,C) labels.

Page 8 gives a sketch of the mathematical role played by this parameter. The symbol used is gamma, see equations 42-47, 49 and 50. Basically it defines a class of SL(2,C) reps and a map from SU(2) to SL(2,C). Then gamma shows up in equation 57 on page 9.
This is the definition of the theory (it is defined by specifying transition amplitudes).

There is an alternative compact definition given in equation 60, where gamma also appears.
=====================

There is no inconsistency that I can see. Gamma is essential in defining the transition amplitudes that define the official version of the theory. And it is also essential in any discussion of the semiclassical limit of the present official version of the theory and in any other aspect of "extracting physics".

You might like to read the "extracting physics" section. It covers a half-dozen topics and is only about 6 pages long.

We shouldn't always be jumping around amongst different people's versions many of which have been superseded or effectively abandoned. More efficient to stick with the one version.

Marcus, I'm trying to be polite. Please stop lecturing us all on what papers/sections we should read before discussing. You've given those references in every thread over and over again, so we got it already. And yes, I can read the equations and see the Immirzi parameter appearing. It clearly plays an important role in formulating the full theory, nevertheless the claim is made in the paper I cited that it drops out in the semiclassical limit.

If you have some actual insight into what is going on, I would really like to hear it. I know you've spent a long time thinking about the theory. However, please stop spamming the thread with passive aggressive suggestions of papers/sections we should read. I'd like to think we're all looking for a little more than simply reading the answer, namely some real analysis and synthesis.

My apologies for the tone of this reply.

 

[atyy]

Interesting, so you're suggesting that perhaps Conrady and Freidel assume something too specialized to see IP dependence?.

Yes, but that's just my guess, based on the assumption that Barrett et al have the state of the art for EPRL (although there are later expositions that are clearer, I don't think anyone has challenged their results), and that FK and EPRL are the same for IP<1.

Perhaps it would be useful to understand to what extent the Planck length, Newton's constant, and the IP are separate entities. They appear multiplying each other in a specific way in the black hole computations. The usual equation is \ell_P^2 = \gamma G_N neglecting some constants (there is typo in one of Rovelli's lectures on this point). Nevertheless, in semi-classical GR what appears directly is G_N while what appears directly in LQG seems to be \ell_P^2. So I continue to feel that unless I'm making some trivial mistake, then somehow the semiclassicl limit should only work if the IP has a specific value. Otherwise we can compute black hole entropy in two different ways and get two different answers.

One thing I'm not clear about is the difference between the classical and semiclassical limit, and which is being taken where. The IP must disappear in the classical limit, and Conrady and Freidel say their result is consistent with that. Funnily, I'm not sure that everyone agrees that LQG needs IP<1 although that's what the black hole entropy calculations suggest. Eg. http://arxiv.org/abs/0909.0939 , which try to adjust EPRL and FK to harmonize better with canonical LQG say "the works that should be and will be considered closer in the spirit of the current paper, are the Freidel-Krasnov model [15] (especially in the range of in which that model does not overlap with EPRL)"

This is interesting, the claim would be that new black hole entropy calculations don't depend on the Immirzi parameter? Or perhaps we should think of the IP as being absorbed into Newton's constant in the semiclassical limit? I shall have to try and track down the paper you mentioned, unless you have a reference off the top of your head.

I wonder if he's thinking of http://arxiv.org/abs/1103.2723 , scanning it quickly it looks like the leading blakc hole entropy term has IP dependence but it the first correction doesn't, which is the IP independence claimed.

I should say that in case the irony hasn't been seen, all the recent Rovelli reviews have been about EPRL.

 

[fzero]

I wonder if he's thinking of http://arxiv.org/abs/1103.2723 , scanning it quickly it looks like the leading blakc hole entropy term has IP dependence but it the first correction doesn't, which is the IP independence claimed.

Yes, that's one of them. I'd cited the paper based on some of the comments I'd read, but had not really figured out what they computed. It seems like their model has the Immirzi parameter and the Chern-Simons level k as free parameters, following http://arxiv.org/abs/1011.2961 I haven't checked the references, so I do not know if there is a physical significance to the level. The 1103.2723 paper claims that one recovers the usual value of the IP from the spherically symmetric model as k\rightarrow\infty.

In any case, the 1011.2961 paper states in the abstract that

"By defining a statistical mechanical ensemble where only the area A of the horizon is fixed macroscopically-states with fluctuations away from spherical symmetry are allowed-we show that it is possible to obtain agreement with the Hawking's area law---S = A/4 (in Planck Units)---without fixing the Immirzi parameter to any particular value: consistency with the area law only imposes a relationship between the Immirzi parameter and the level of the Chern-Simons theory involved in the effective description of the horizon degrees of freedom. "

and the 1103.2723 paper computes the leading correction to the area law.

Without knowing the fundamental significance of the level in these calculations, I wouldn't begin to consider the implications of the results.

The other paper I was thinking of was this one:

http://arxiv.org/abs/1103.2971
Gravity as a constrained BF theory: Noether charges and Immirzi parameter
R. Durka, J. Kowalski-Glikman
5 pages
(Submitted on 15 Mar 2011)
"We derive and analyze Noether charges associated with the diffeomorphism invariance for the constrained SO(2,3) BF theory. This result generalizes the Wald approach to the case of the first order gravity with a negative cosmological constant, the Holst modification and topological terms (Nieh-Yan, Euler, and Pontryagin). We show that differentiability of the action is automatically implemented by the the structure of the constrained BF model. Finally, we calculate the AdS--Schwarzschild black hole entropy from the Noether charge and we find that, unexpectedly, it does not depend on the Immirzi parameter."

They suggest that the IP is somewhere hidden in the translation between microscopic variables and the effective ones that they're using.

 

[marcus]

...
They suggest that the IP is somewhere hidden in the translation between microscopic variables and the effective ones that they're using.

They cite a really interesting 2007 paper by Ted Jacobson. I think someone already gave the link but I will get it. As I recall he put the Loop community on notice that they would eventually have to face the problem of G running. And this would come out in the black hole analysis.
That is one of those papers where you wait for years for the other shoe to drop. He has written more than one of those.
T. Jacobson, “Renormalization and black hole entropy in Loop Quantum Gravity,” Class. Quant. Grav. 24 (2007) 4875-4879. [arXiv:0707.4026 [gr-qc]].
http://arxiv.org/abs/0707.4026
Renormalization and black hole entropy in Loop Quantum Gravity
Ted Jacobson
8 pages
(Submitted on 26 Jul 2007)
"Microscopic state counting for a black hole in Loop Quantum Gravity yields a result proportional to horizon area, and inversely proportional to Newton's constant and the Immirzi parameter. It is argued here that before this result can be compared to the Bekenstein-Hawking entropy of a macroscopic black hole, the scale dependence of both Newton's constant and the area must be accounted for. The two entropies could then agree for any value of the Immirzi parameter, if a certain renormalization property holds."

 

[marcus]

This "Immirzi puzzle" topic is raised by Rovelli on page 16 of his December review paper and discussed briefly. You might be interested in what he has to say about it, if you haven't already read this. It may be very similar to what has already been said in some posts in this thread, but differences in perspective (if there are any) could be interesting.

Of course he cites the Jacobson 2007 paper about renormalization and BH entropy (here reference [144].

http://arxiv.org/abs/1012.4707
Loop quantum gravity: the first twenty five years

==quote 1012.4707==
However, the result is not entirely satisfactory in my opinion. It is not strange that a fundamental parameter in the theory could have a peculiar value such as γo: we do not understand the origin of other fundamental constants, such that the fine-structure constant. But it is strange, and perplexing, that there be such a peculiar parameter in the theory, which then cancels exactly with a number that characterizes a complicated statis- tical counting, in such a way to give a round number such as 4 in (43).¹⁷ I think that the sense that there is something important which is not yet understood is unavoidable.

17 In addition, as pointed out by Ted Jacobson [144], radiative correction could play a role, affecting the Area observable and the coupling constants. In particular, the G entering (43) is the Newton constant at large distance, while the G entering (44) might be the Newton constant G_Plank at the Planck scale. So that we should rather pose

γ = γ_oG_Plank/G (46)

and the numerical value of γ_o could perhaps reappear in the relation between Plank scale and infrared physics.
==endquote==

My apologies for the tone of this reply.

I thought that was an excellent reply! Expressed values we both share and very polite given the circumstances. I think both you and Fzero have read the recent LQG papers and some one of you even pointed out a typo! I think in the February "Lectures" paper. I appreciate your recognizing that there was a reconstitution of Loop in 2010 and proceeding from there.

My reciprocal apologies for strident repetition of this fact!

What you said about "we get it already" was very welcome indeed! For anyone else reading the thread, the papers we are talking about that redefine LQG as a theory (this is not for Atyy, Fzero, PhysicsMonkey since all are well known to them) are:
http://arxiv.org/abs/1102.3660
http://arxiv.org/abs/1012.4707
http://arxiv.org/abs/1010.1939

 

[fzero]

Thanks for pointing out the Jacobson paper. Some digging actually turned up a paper by Susskind and Uglum http://arxiv.org/abs/hep-th/9401070 that makes essentially the same point about the interplay between renormalization of the BH entropy and gravitational coupling. Further evidence for this is described by Larsen and Wilczek in http://arxiv.org/abs/hep-th/9506066 Both papers discuss the result in the context of matter coupled to canonical gravity in the limit of large BH mass.

 

[atyy]

marcus, why do you say there was a reconstitution in 2010? The 2010 papers are reviews - the reconstitution was in 2007/2008 with the EPR model (now superseded), and then FK and EPRL, which overlap for IP<1, as well as the demonstration of nice asymptotic properties by Conrady and Freidel, and Barrett et al. EPRL is the subject of all the 2010/2011 reviews.

Also, old LQG is still in play, Rovelli does cite Kaminski et al in the same breath that he cites EPR,FK and EPRL (http://arxiv.org/abs/1102.3660 , p10, just after Eq 59, "This vertex amplitude (56-57) has been found independently by different research groups [30-35]"). Kaminski et al try to fix EPRL/FK to agree with canonical LQG. The whole black hole business is also in canonical LQG, as is most LQC, even the Ashtekar and Henderson stuff. Only Vidotto's LQC tries to begin from EPRL.

 

[marcus]

marcus, why do you say there was a reconstitution in 2010? ...

Well should we start a separate thread? So as not to clutter up PM's thread about the Immirzi? Or can you propose a thread where this question is germane or already being discussed?

You say what we should do, if we should move this side-discussion somewhere.

• The 2010 reformulation has no spacetime manifold.
• The exposition stresses striking analogies with BOTH lattice QCD and Feynman diagram QED.
• In the 2010-2011 Rovelli gives a particular Hilbertspace, then he gives three equations, then he says "This is the theory." Or he says, "This defines the theory."
• He doesn't call it EPRL and the way vertex amplitude is computed is different from how I recall EPRL.
• He calls it "Loop Gravity".

AFAIK all those different acronyms EPR, EPRL, FK, EPRL-FK, merely refer to different proposed ways of calculating a spinfoam vertex amplitude. That is not a whole theory.
Vertex amplitudes are crucial but you still have to back off and decide how you are going to formulate transition amplitudes between spin network states of geometry.

Then there is the question of coherent states. The new formulation comes with holomorphic coherent states. It also comes with a rigorous proof of lorentz covariance. It comes with a couple of rather elegant ways to calculate the vertex amplitude which are NOT the original EPR or EPRL or FK, ways as far as i know. I don't see any 12j symbols. What I see instead is a map from SU(2) group representations to SL(2,C) representations.
I'm not saying you can't go back and forth and establish EQUIVALENCES between these things. What I'm saying is that the 2010 reformulation looks much more substantial and more like a theory to me. BTW also more mathematically beautiful.

And Rovelli calls it a theory, rather than an approach. 2010 is the first time I recall him saying "This defines the theory."

So I call it 2010 reformulation rather than 2007 or 2008 or whatever because that was the year the pieces came together and he ran the theory flag up the mast. Now it could be shot down in various dignified ways---there is something there to shoot down. Maybe it will be and maybe it won't be.

Maybe this storm over the Immirzi and the Black Hole entropy will destroy it, and maybe it won't.

Please tell me if I'm missing anything important, Atyy. And if you still want to discuss and say I should use the term "EPRL" and the date 2007 or 2008, then just say and we can start a separate thread. In some sense it's partly just a matter of taste.

Meanwwhile, the current Immirzi emergency is potentially exciting, isn't it? Alarm bells going off. I have the highest regard for both Jacobson and Kowalski-Gllkman, so I think something transformative may come out of it.

 

[atyy]

In http://arxiv.org/abs/0902.0351 which is the follow up to http://arxiv.org/abs/0809.2280 , Eq 133 contains the Immirzi parameter. Their comment on the relationship to the result without the Immirzi parameter is "One can show (directly or using the results of [5]) that these terms drop out when the saddle point approximation is applied to a bulk region consisting of several 4–simplices."

In http://arxiv.org/abs/1003.1886 , Fairbairn comments on the relationship between his calculation (Barrett et al) and that of Conrady and Freidel's "In this paper, we summarise the results obtained in [1, 2, 3], where an asymptotic analysis of the 4-simplex amplitudes for the Ooguri model [4] of topological BF theory and for both Euclidean and Lorentzian versions of the EPRL model [5] of quantum gravity was performed. For an asymptotic analysis of the whole amplitude Z(M) for a closed manifold M of Euclidean signature see [6, 7]."

So my guess is that the large spin limits taken here involve assumptions that make it not a black hole (although still involving the IP in some cases). In http://relativity.phys.lsu.edu/ilqgs/panel050509.pdf , p3, Ashtekar, following Perez, says he expects an isolated horizon to be dominated by small spins.

 

[marcus]

Atyy, thanks for the links and summaries. It's a pleasure being able to connect with an extra pair of eyes and memory for making connections. I'm still (ploddingly) assimilating what I quoted from Rovelli's december review paper, the section on BH entropy that referred to Jacobson's 2007 paper (one that's been in the back of my mind since it came out, waiting for the other shoe to drop.)
Here is the passage I quoted earlier:

http://arxiv.org/abs/1012.4707 (page 17)
Loop quantum gravity: the first twenty five years

==quote 1012.4707==
However, the result is not entirely satisfactory in my opinion. It is not strange that a fundamental parameter in the theory could have a peculiar value such as γ_o: we do not understand the origin of other fundamental constants, such as the fine-structure constant. But it is strange, and perplexing, that there be such a peculiar parameter in the theory, which then cancels exactly with a number that characterizes a complicated statistical counting, in such a way to give a round number such as 4 in (43).¹⁷ I think that the sense that there is something important which is not yet understood is unavoidable.

17 In addition, as pointed out by Ted Jacobson [144], radiative correction could play a role, affecting the Area observable and the coupling constants. In particular, the G entering (43) is the Newton constant at large distance, while the G entering (44) might be the Newton constant G_Planck at the Planck scale. So that we should rather pose

γ = γ_oG_Planck/G __________________ (46)

and the numerical value of γ_o could perhaps reappear in the relation between Planck scale and infrared physics.
==endquote==

Then there is the fact that the February papers, in many respects an excellent complete summary of the theory, omits all discussion of BH. I'm curious to see how this gets resolved.

 

[atyy]

Maybe the calculated entropy is more like an entangelment entropy, in which case it would be a correction to the BH entropy, and not required to take such a special value?

Corichi's review http://arxiv.org/abs/0901.1302 refers to http://arxiv.org/abs/hep-th/0501103 for different views of what's actually being calculated.

 

[marcus]

Maybe the calculated entropy is more like an entangelment entropy, in which case it would be a correction to the BH entropy, and not required to take such a special value?

Corichi's review http://arxiv.org/abs/0901.1302 refers to http://arxiv.org/abs/hep-th/0501103 for different views of what's actually being calculated.

I can't comment, hopefully someone else will be able to carry your idea further. However in line with the topic of this thread, the Immirzi,
there is what I regard as a really extraordinary talk by James Ryan here:
http://relativity.phys.lsu.edu/ilqgs/
Simplicity Constraints and the Immirzi Parameter in Discrete Quantum Gravity
It was given 12 April. The audio file is good quality. Here is the PDF
http://relativity.phys.lsu.edu/ilqgs/ryan041211.pdf
Ryan is reporting work done with Bianca Dittrich at AEI.
(He got his PhD at Cambridge with Oriti and then went to Perimeter, where he was Hossenfelder's officemate for a while. Has collaborated with Livine several times IIRC.)

Also I think you may have seen this one, I did not take enough time to understand and could not immediately make much out. But it's also something recent about the Immirzi.
http://arxiv.org/abs/1104.4028
Perturbative quantum gravity with the Immirzi parameter
Dario Benedetti, Simone Speziale
(Submitted on 20 Apr 2011)
"We study perturbative quantum gravity in the first-order tetrad formalism. The lowest order action corresponds to Einstein-Cartan plus a parity-odd term, and is known in the literature as the Holst action. The coupling constant of the parity-odd term can be identified with the Immirzi parameter of loop quantum gravity. We compute the quantum effective action in the one-loop expansion. As in the metric second-order formulation, we find that in the case of pure gravity the theory is on-shell finite, and the running of Newton's constant and the Immirzi parameter is inessential. In the presence of fermions, the situation changes in two fundamental aspects. First, non-renormalizable logarithmic divergences appear, as usual. Second, the Immirzi parameter becomes a priori observable, and we find that it is renormalized by a four-fermion interaction generated by radiative corrections. We compute its beta function and discuss possible implications. The sign of the beta function depends on whether the Immirzi parameter is larger or smaller than one in absolute value, and the values plus or minus one are UV fixed-points (we work in Euclidean signature). Finally, we find that the Holst action is stable with respect to radiative corrections in the case of minimal coupling, up to higher order non-renormalizable interactions."

 

[atyy]

Thanks for the pointer to Ryan's talk.

where he was Hossenfelder's officemate for a while.

How do you know things like this?

 

[marcus]

Thanks for the pointer to Ryan's talk.
How do you know things like this?

I'd like to hear any reaction you have to Ryan's talk. You have paid attention to both Dittrich's and Livine's work and he has collaborated with them IIRC, at least currently is with Dittrich.
These people are breaking new ground, I think---going ahead on their own path.

About Hossenfelder, I just remember her saying something about Ryan in her blog, I found it:
http://backreaction.blogspot.com/2009/10/seminar-at-Albert-einstein-institute.html
It is right near the end of the post and doesn't say explicitly at Perimeter but this is probably to be understood. She is an outspoken person who helps to humanize frontline research and I appreciate this.
For any latecomer here is Ryan's talk:
http://relativity.phys.lsu.edu/ilqgs/
Simplicity constraints and the role of the Immirzi parameter in quantum gravity
http://relativity.phys.lsu.edu/ilqgs/ryan041211.pdf
Here are a couple of Dittrich et al papers
http://arxiv.org/abs/1006.4295
http://arxiv.org/abs/1103.6264
There's a snap of the scientist in question at the Perimeter site:
http://www.perimeterinstitute.ca/index.php?option=com_content&task=view&id=30&Itemid=72&pi=4764

 

[Sardano]

I would like to discuss a puzzle I'm wondering about in loopy approaches to quantum gravity.

The puzzle is roughly as follows:
The Immirzi parameter (IP) is a strange constant that appears in loopy approaches. Calculations of black hole entropy in loopy approaches seem to need to fix the IP to be a particular value to agree with semi-classical entropy calculations. On the other hand, http://arxiv.org/abs/0809.2280 suggests that the IP plays little role in establishing the semi-classical limit of certain spin foam models. So what gives? Have I misunderstood something elementary? Will we find that the IP is given by the black hole value via other means? If not, what do the loopy approaches describe when the IP is not tuned to the black hole value? It almost seems impossible to have a semi-classical limit of GR for all IP, but only be able to reproduce the semi-classical black entropy for a particular IP.

Please let's keep the discussion to the science as much as possible. Thanks!

Maybe all this means that LQG is wrong and it can't even give the correct answer to the entropy of a Black Hole.

 

[suprised]

Maybe all this means that LQG is wrong and it can't even give the correct answer to the entropy of a Black Hole.

Apparently it cannot, as of today, give an answer this question, because one has to put it in by hand. I guess that's why many people don't take this point serious. But at least the area law seems to come out, which is encouraging because this is one of the most important features of QG.

 

[atyy]

Apparently it cannot, as of today, give an answer this question, because one has to put it in by hand. I guess that's why many people don't take this point serious. But at least the area law seems to come out, which is encouraging because this is one of the most important features of QG.

I'm wondering from the way it's calculated, is it more like the entanglement entropy, and so more like a correction to the Bekenstein-Hawking entropy than the Bekenstein-Hawking entropy itself?

 

[Physics Monkey]

Maybe all this means that LQG is wrong and it can't even give the correct answer to the entropy of a Black Hole.

I would say that LQG is probably a consistent mathematical structure, although unlike string theory it does not have as clear a relation to what we would call classical gravity. Thus "wrong" would only mean that it doesn't describe the particular thing we call quantum gravity in our world. Nevertheless the theory may still be quite interesting/useful/stimulating and merit attention. String theory certainly has met this qualification already, even if it has nothing ultimately to do with our particular universe.

Also, I think its fair to say that LQG can give black hole entropy, it just requires a little extra information (at the current level of development). As surprised suggested, I think the area law is the tough bit, although I agree that getting the coefficient right is also important. It would be much worse for the theory if the area law had not come out or if the parameters of the theory could not be adjusted in a way consistent with the semiclassical result. Only then would I say that LQG cannot give the correct answer to black hole entropy.

 

[tom.stoer]

Let me reawaken this thread.

I know that BH entropy can be derived from LQG in agreement with Bekenstein-Hawking by fixing the Immirzi parameter to a specific value.

I know that the Imirzi parameter enters the construction of spin networks / spin foams and that there are certain "subclasses" of LQG related to some special values i, 0, 1, ∞; ...

Looking at the classical Nieh-Yan / Holst action one can start a renormalization group approach a la "asymptotic safety" taking into account the couplings κ (Newton's constant), γ (Barbero-Immirzi), Λ (cosmological constant) and others - which are hopefully driven to zero by the renormalization group flow. Here different "theories" are not distinguished by different values but by different trajectories in the γκΛ-space.

How are these different approaches related?
How does this renormalization group flow change when fermions are added?

I know that with SU(2)_q defomed spin networks Λ is related to the deformation parameter q.

How does this fit together with the renormalization group flow?

 

[tom.stoer]

push ...

 

[Demystifier]

A recent calculation suggests that the black-hole entropy in LQG does NOT depend on the Immirzi parameter:
http://xxx.lanl.gov/abs/1107.1320
More precisely, the entropy is A/4 (Bekenstein-Hawking, Immirzi independent) plus a topological Immirzi-dependent term which does not depend on the surface A.

This seems to be a very surprising result, but even more surprising is that Marcus hasn't already drawn our attention to this paper. :-)

 

[tom.stoer]

This seems to be a very surprising result, but even more surprising is that Marcus hasn't already drawn our attention to this paper. :-)

The fact that marcus has not yet commented on this paper proves its nonexistence ...

... honestly, thanks for the reference; I have to think about it ...



That would change my list slightly, but the main questions are not affected:

I know that the Imirzi parameter enters the construction of spin networks / spin foams and that there are certain "subclasses" of LQG related to some special values i, 0, 1, ∞; ...

Looking at the classical Nieh-Yan / Holst action one can start a renormalization group approach a la "asymptotic safety" taking into account the couplings κ (Newton's constant), γ (Barbero-Immirzi), Λ (cosmological constant) and others - which are hopefully driven to zero by the renormalization group flow. Here different "theories" are not distinguished by different values but by different trajectories in the γκΛ-space.

How are these different approaches related?
How does this renormalization group flow change when fermions are added?

I know that with SU(2)_q defomed spin networks Λ is related to the deformation parameter q.

How does this fit together with the renormalization group flow?

 

[marcus]

I logged the Ghosh Perez paper in the bibliography when it came out. Thanks Demy! It looks as if it could be important.

Alejandro gave an invited talk (BH Entropy and Chern-Simons) on 26 May at the Madrid Loops conference
http://loops11.iem.csic.es/loops11/index.php?option=com_content&view=article&id=184 At the very end, right before the QA, he briefly mentioned a connection between CS level and immirzi parameter.

The slides PDF and video of the talk are available. I looked at the slides and did not see these Ghosh Perez results, nor did I see reference to collaboration with Ghosh. Perhaps the paper was still in the works, so Alejandro had no reason to mention it. btw Amit Ghosh ( http://www.phys.psu.edu/people/display/?person_id=166 ) has a number of papers on BH entropy. PhD Calcutta 1997, postdoc at Penn State (among other places), visitor Marseille during May 2011, homebase at Calcutta. Someone to be aware of. The Marseille visitor list ( http://www.cpt.univ-mrs.fr/~quantumgravity/ ) gives some idea of the level of activity and collaboration.

 

[bcrowell]

As a total LQG ignoramus, it seems to me that there might be multiple possible ways of interpreting the Ghosh-Perez result. On the surface, it seems inconsistent with previous results, which claimed to be able to fix the IP. So:

(A) LQG has multiple methods for calculating entropy, they give different results, and there is no way of telling which is right, except by reference to some other theory; or
(B) Ghosh and Perez have given (or someone else can give) a clear and compelling physical explanation for why their method is right and previous methods were wrong.

If it's A, LQG has serious problems. If it's B, LQG-ers should be dancing in the streets.

Ghosh and Perez do seem to make a serious effort to tell a compelling physics story in their paper, but it's not a story whose merit I can judge with my level of (lack of) expertise.

 

[marcus]

... LQG-ers should be dancing in the streets.
...

there have been a number of indications that it would be nice if the IP were free to run.

So if the Ghosh Perez results are confirmed a lot of people will be happy.

If I'm not mistaken they show that the familiar value is recovered in a certain limit.

But the exact value of the IP is not the main thing. What they primarily do is they get the S = A/4 to fist order without the IP entering in. That is a stronger result. Before, one had to adjust something to get that equality. Now one has it plain and simple: muchmuch better.

BTW the sense that IP should run or be involved in renormalization appeared already in a 2007 paper by Ted Jacobson (major QG guru with a lot of foresight) http://arxiv.org/abs/0707.4026 made an impression on me so I've been waiting for the other shoe to drop. This could be it, and it might not. Also there may have been something by Kowalski-Glikman in the past year, but my memory of that is dim, can't be sure.

Anyway it has always been awkward that the IP appeared in S = A/4 at leading order, because that fixed it. Ghosh Perez refer to this as a kind of vulnerability. They may have cured that, freeing it up.

I hope it will be confirmed. It's exciting, as you point out. I don't know enough to offer an opinion about the validity, and how it will hold up. I have to wait and see, hoping.

 

[Demystifier]

As a total LQG ignoramus, it seems to me that there might be multiple possible ways of interpreting the Ghosh-Perez result. On the surface, it seems inconsistent with previous results, which claimed to be able to fix the IP. So:

(A) LQG has multiple methods for calculating entropy, they give different results, and there is no way of telling which is right, except by reference to some other theory; or
(B) Ghosh and Perez have given (or someone else can give) a clear and compelling physical explanation for why their method is right and previous methods were wrong.

If it's A, LQG has serious problems. If it's B, LQG-ers should be dancing in the streets.

Ghosh and Perez do seem to make a serious effort to tell a compelling physics story in their paper, but it's not a story whose merit I can judge with my level of (lack of) expertise.

I disagree with only one statement: that you are a total LQG ignoramus.

 

[marcus]

Since the last few posts have been about the new paper by Ghosh Perez, I'll copy the abstract here for reference---and note a related paper by Kowalski-Glikman.

58]http://arxiv.org/abs/1107.1320
Black hole entropy and isolated horizons thermodynamics
Amit Ghosh, Alejandro Perez
(Submitted on 7 Jul 2011)
We present a statistical mechanical calculation of the thermodynamical properties of (non rotating) isolated horizons. The introduction of Planck scale allows for the definition of an universal horizon temperature (independent of the mass of the black hole) and a well-defined notion of energy (as measured by suitable local observers) proportional to the horizon area in Planck units. The microcanonical and canonical ensembles associated with the system are introduced. Black hole entropy and other thermodynamical quantities can be consistently computed in both ensembles and results are in agreement with Hawking's semiclassical analysis for all values of the Immirzi parameter.
5 pages

My comment would be that the reason you can have a horizon temp be independent of the BH mass is that this temperature is measured by an observer hovering down near the horizon----not by somebody at infinity.

One important aspect of their result is that they get S = A/4 without having to adjust the Immirzi parameter.

So the IP is still free and may play a role in renormalization or relation to the cosmological constant. This is a big change. You used to have to adjust the IP to a fixed value in order to recover S = A/4. I noticed a hint of this back in March 2011, with a paper by Jerzy K-G and Remy Durka.

Also there may have been something by Kowalski-Glikman in the past year,...

http://arxiv.org/abs/1103.2971
Gravity as a constrained BF theory: Noether charges and Immirzi parameter
R. Durka, J. Kowalski-Glikman
(Submitted on 15 Mar 2011 (v1), last revised 30 May 2011 (this version, v2))
We derive and analyze Noether charges associated with the diffeomorphism invariance for the constrained SO(2,3) BF theory. This result generalizes the Wald approach to the case of the first order gravity with a negative cosmological constant, the Holst modification and topological terms (Nieh-Yan, Euler, and Pontryagin). We show that differentiability of the action is automatically implemented by the the structure of the constrained BF model. Finally, we calculate the AdS--Schwarzschild black hole entropy from the Noether charge and we find that, unexpectedly, it does not depend on the Immirzi parameter.
6 pages,... to be published in Physical Review D

Jerzy K-G would be familiar to many of us, but his PhD student Durka perhaps less, so here is Remy's homepage as introduction:
http://www.ift.uni.wroc.pl/~rdurka/
In like manner, people may be less familiar with Perez' co-author Amit Ghosh, so I'll repeat what I said earlier:
Amit Ghosh ( http://www.phys.psu.edu/people/display/?person_id=166 ) has a number of papers on BH entropy. PhD Calcutta 1997, postdoc at Penn State (among other places), visitor Marseille during May 2011, homebase at Calcutta... The Marseille visitor list ( http://www.cpt.univ-mrs.fr/~quantumgravity/ ) gives some idea of the level of activity and collaboration [now in progress at Marseille].

 

[Finbar]

Its perhaps good to point out that if one can show that any proposed UV completion of general relativity has the right semi-classical limit it must reproduce the Hawking-Bekenstein entropy in this limit to leading order. So the string theory calculation that recovers it was a for gone conclusion once it was shown that string theory has the right semi-classical limit.

The converse is not true though. Reproducing the Hawking-Bekenstein entropy does not ensure that the theory has the right semi-classical limit.

What this means is that the real challenge to LQG is to get the right semi-classical limit.
If the value they get for the number of microstates within some calculation is not the
HB one then this might only mean that they have not yet taken the semi-classical limit.
Somehow LQG researches need to understand how the parameters in their theory flow to the IR.

The final comment in the R. Durka, J. Kowalski-Glikman seems to agrees with me

In both cases it remains to be understood in details how the proposed mechanisms work. This question is related to the notorious problem of the semiclassical limit of Loop Quantum Gravity, and it seems that without controlling this limit one cannot make any definite conclusions.

 

[marcus]

Its perhaps good to point out that if one can show that any proposed UV completion of general relativity has the right semi-classical limit it must reproduce the Hawking-Bekenstein entropy in this limit to leading order. So the string theory calculation that recovers it was a for gone conclusion once it was shown that string theory has the right semi-classical limit.
...

I'm something of an Andy Strominger fan. I give him a lot of credit for proving S=A/4 in the special case of extremal black hole. Not a trivial result, at the time, I think.
http://arxiv.org/abs/hep-th/9601029
Microscopic Origin of the Bekenstein-Hawking Entropy
A. Strominger, C. Vafa

I suspect you know what you are talking about, though---often a lot is in how we define our terms.
=========================

However this is a bit off-topic. The topic here is the Immirzi Parameter and its role in LQG.

 

[marcus]

This thread is about the Immirzi parameter (IP) and its role in LQG and it looks like we are seeing a NEW TAKE on the Immirzi emerge, notably with this paper by Ghosh and Perez that we were discussing on the previous page:

Since the last few posts have been about the new paper by Ghosh Perez, I'll copy the abstract here for reference---and note a related paper by Kowalski-Glikman.

58]http://arxiv.org/abs/1107.1320
Black hole entropy and isolated horizons thermodynamics
Amit Ghosh, Alejandro Perez
(Submitted on 7 Jul 2011)
We present a statistical mechanical calculation of the thermodynamical properties of (non rotating) isolated horizons. The introduction of Planck scale allows for the definition of an universal horizon temperature (independent of the mass of the black hole) and a well-defined notion of energy (as measured by suitable local observers) proportional to the horizon area in Planck units. The microcanonical and canonical ensembles associated with the system are introduced. Black hole entropy and other thermodynamical quantities can be consistently computed in both ensembles and results are in agreement with Hawking's semiclassical analysis for all values of the Immirzi parameter.
5 pages

My comment would be that the reason you can have a horizon temp be independent of the BH mass is that this temperature is measured by an observer hovering down near the horizon----not by somebody at infinity.

One important aspect of their result is that they get S = A/4 without having to adjust the Immirzi parameter.

So the IP is still free and may play a role in renormalization or relation to the cosmological constant. This is a big change. You used to have to adjust the IP to a fixed value in order to recover S = A/4...

=======
I like the appearance of a chemical potential here, energy associated with spin net punctures---i.e. with increasing by one the number of links of the spin network passing through the horizon. The chemical potential µ_∞ is this potential seen by an observer at infinity. They also use a µ which is measured by a nearby observer, hovering close to the horizon. This µ is negative up to a critical value of the Immirzi, which I think is around 0.274.

So the chemical potential being negative (as long as the IP is less than its critical value) means that more punctures are favored. The system will relax by developing a spin network state which has more punctures.

This is also favored entropically.

Holding the area constant while increasing the number N of punctures means having more puncture colored with lower spins----more spin = 1/2 labels---subject to whatever constraints of geeometry, other things being equal.

It's an intriguing paper, to say the least! I think one way that this is an advance is they recognize that as defined the usual BH event horizon is unphysical. In a quantum world one does not have access to some idealized "past of future null infinity" (all the more because the thing is evaporating).
So they don't use the unphysical EH----they use the IH (isolated horizon) concept. That alone helps to make this paper different from some of its precursors. Finbar I expect you are thoroughly familiar with this, but in case others are reading, here is a reference:

http://arxiv.org/abs/gr-qc/0407042
Isolated and dynamical horizons and their applications
Abhay Ashtekar, Badri Krishnan
(Submitted on 13 Jul 2004)
Over the past three decades, black holes have played an important role in quantum gravity, mathematical physics, numerical relativity and gravitational wave phenomenology. However, conceptual settings and mathematical models used to discuss them have varied considerably from one area to another. Over the last five years a new, quasi-local framework was introduced to analyze diverse facets of black holes in a unified manner. In this framework, evolving black holes are modeled by dynamical horizons and black holes in equilibrium by isolated horizons. We review basic properties of these horizons and summarize applications to mathematical physics, numerical relativity and quantum gravity. This paradigm has led to significant generalizations of several results in black hole physics. Specifically, it has introduced a more physical setting for black hole thermodynamics and for black hole entropy calculations in quantum gravity; suggested a phenomenological model for hairy black holes; provided novel techniques to extract physics from numerical simulations; and led to new laws governing the dynamics of black holes in exact general relativity.
77 pages, 12 figures. Published in Living Reviews of Relativity

 

[marcus]

From page 4 of Ghosh Perez
Classically, the only natural value of the chemical potential is zero, which implies
1 = ∑(2j + 1) exp(−2πγ√[j(j + 1)]).
(My comment: This is what determines γ_o the critical value of γ.)
Some background on the number 0.274 is here:
http://arxiv.org/abs/0906.4529
See equation (9) on page 4. A more precise value and its square root:
(0.274067...)^1/2 = 0.5235...