Map of nonstring QG (as of November 2007)

[marcus]

QG has several approaches developing rapidly and it's not easy to maintain perspective.
I'll update a rough outline map made earlier. We can use it to help know what papers to expect during the next couple of months and what developments to be prepared for.

A. Three main sectors of Loop-community work:

1. Marseille new vertex
suggested review = latest Rovelli et al (what I think will probably be QG paper of the year)

2. Penn State cosmology
suggested review = Ashtekar's latest
new feature = Bojowald on big bang nucleosynthesis

3. Perimeter dynamic topology
both geometry and matter emerge from topology of fourvalent braid network states
these states evolve by local moves which change how neighbor vertices are connected.
No current review, but see recent papers by Smolin and Wan.
Work in preparation by Bilson-Thompson, Hackett, Kauffman
(look for "Sun-Jon-Louis" paper)

B. Other approaches to watch (several have no minimal scale, in other words scale -> 0 )

1. Legoblock path integral
Loll's review just came out
(CDT let's the size of the blocks go to zero)

2. Running couplings--going with the flow
Percacci's review, "Asymptotic Safety"
(Reuter-Percacci let the energy scale k go to infinity)

3. Hodge star gravity, where the Hodge dual replaces metric d.o.f.
Krasnov's review just came out "Non-metric gravity: a status report"
(see section 3 on Renormalizability)

4. Garrett Lisi's E8 gravity+matter----representing geometry + matter with an E8 connection

C. Dark horses:

1. Pereira and Aldrovandi's deSitter GR---a bold idea that runs a severe risk of being falsified by TeV gammaray telescope data. A fairly complete P and A paper on deS GR just appeared. So we have an up-to-date account of the status of their theory. Now it's up to astronomers to confirm or refute.

2. Jesper Grimstrup LQG + NCG---another risky project: putting Connes standard particle model into LQG.
Last paper was in 2006. Hopefully something from Aastrup and Grimstrup before long.

====================

Have review or status report papers for 2007 in these cases:
A1. (Rovelli group et al)
A2. (Ashtekar Bojowald et al)

B1. (Loll group)
B2. (Reuter Percacci et al)
B3. (Krasnov)
B4. (Lisi)

C1. (Pereira Aldrovandi)

Do not have 2007 review or status report in these cases:

A3. (Smolin group)
C2. (Grimstrup...)
=================

A couple of things to think about: For one, how this is going to look around 1 July when there is the big international QG conference in UK called "QG² 2008"?
The main organizer John Garrett will almost certainly have a different map in mind. Some of the people in my outline here will give invited plenary talks at QG^2. Which ones, and specifically about what?

For another, which of these approaches can merge constructively, or be shown to be equivalent?

For example, Smolin dynamic topology approach uses FOURvalent vertices to describe a braided webwork from which geometry and matter should emerge. In a fourvalent web one can replace every vertex by a tetrahedron, and have something looking like a LOLL setup. So at least a superficial resemblance, but nothing said here comparing the dynamics of moves by which the webwork and the triangulation evolve. Pachner moves come up in both cases, but don't jump to conclusions At this point the two approaches look quite different.

For example Pereira and Aldrovandi approach has a term called the conformal current related to how rapidly space is expanding. In several versions of LQG one needs to control the amplitude with which new vertices are created. If P&A should turn out to be compatible with spinnetwork dynamics, does their conformal current give a handle on that applitude?

P&A seem to have a mathematically nice way of doing what used to be called deformed special relativity (DSR). They don't mess with deforming special, they go right to general and use deSitter in place of Lorentz/Poincaré. The results are a little hair-raising at first sight but very interesting. It might actually be highly suitable as a classical limit for some version that Smolin Rovelli et al are working on.

So convergence is another thing to think about in the context of this map.

 

[jimgraber]

Hi Marcus,
Thanks for a really informative post, I really appreciate this type of cogent summary. I also greatly appreciate your keeping up the important papers running thread.

Jumping back to a recent discussion in the graviton thread, you have just listed nine approaches. One thing I would like to know is, "Which of these approaches are graviton friendly, i. e. include a graviton or some near equivalent? Which ones are, on the contrary, proposing some substantially different alternative to the graviton? And which ones are still not yet advanced enough to definitely put in either category?

I'll try to start on this classification in my next post.

Jim Graber

 

[jimgraber]

Rovelli group talks about graviton propagator all the time, so A1 is graviton friendly for sure. Your previous quote of Loll saying the graviton has failed as a fundamental basis is pretty negative, so B1 probably belongs in the anti-graviton group, although I think based on their own statements, you could also argue for group three, the "Can't tell yet" group.
Now I will have to go and search the arXiv some more to see if my memory of other groups is correct, and of course, I have no idea about some of the newer groups.
Best.
Jim Graber

 

[Chronos]

A good synopsis, marcus. All these ideas are worthy. I'm partial to Smolin's approach, but time will tell.

 

[jimgraber]

I couldn’t find a place where Lisi mentions the graviton in his new paper, unlike the Higgs, the curvature, and the connection, which he mentions frequently. But he also mentions the usual SO(3,1) Lie group or Lorentz group, and the so(3,1) Lie algebra, ans I find elsewhere that the graviton is one of the generators of the gravitational so(3,1).
So I would put Lisi in the graviton friendly group, absent contrary evidence.

Astekar spends a whole section on recovering the graviton propagator in his most recent LQG summary, so Ashtekar LQG is definitely graviton friendly.

Bojowald LQC is a different matter, and one I don’t even pretend to understand:
The newer LQC is at one point described as a simplification of the full LQG, this would argue it should also be graviton friendly.
However, at another point it is stated that the two theories share no common nonzero algebraic elements. Given the connection of the graviton with the Lie algebra generator, this makes me wonder. Also, I could find no explicit mention of the graviton in the LQC review. As far as I can tell from my very brief review LQC is independent of graviton issues, although standard GR and curvature emerges at long distances. My best guess is this theory is compatible with but not dependent on gravitons.
This suggests to me that A2 should be split into LQG and LQC, which seem to really be two separate approaches, although they share some heritage.

Also along these lines, what about Thiemann? Doesn’t he count as another separate approach? If not, which one of your groups does he fit in?

Konopka, Markopoulou and Smolin directly say that they have not yet attempted to reproduce gravitons, but it could perhaps be done by using LQG as a guide. So that falls squarely in group three as far as completed work is concerned, but seems to me to fall into group one as far as attitude is concerned.

In fact, I asked Lee what the braid representation of a graviton was during the public Q+A after his presentation at the APS meeting in Jacksonville. As far as I can remember, he said something like “not done yet, but we have several possible ideas how to do it.”
He said something about the unbraid, but I can’t remember what.

Its very late and I’ll stop here I’ve read far too many papers I don’t really understand>
Take everything in this post with a ton of salt.
Good night.
Jim Graber

 

[Coin]

Hi, don't know whether this is the right place to ask this but something I've been trying to understand about the LQG program: What generally is the difference between the spinfoam and pre-spinfoam approaches to LQG, and do they actually represent different approaches or just a different formalism for describing the same things? Is the pre-spinfoam approach completely abandoned, or is it still used alongside spinfoams, or does it just represent a separate branch of LQG at this point? Do these questions make sense?

I'd gotten the impression in a couple of places that the spinfoam approach was somehow a break from the early LQG spin-networks approach, and that the difference had to do with lorentz invariance. But this is a very vague impression and I've still had trouble finding an explanation of what exactly the difference between a spinfoam and a spin network is.

 

[ccdantas]

Hi Marcus,

Very good "map". How would you classify Eyo Eyo Ita's work?

Christine

 

[jimgraber]

Two more important (in my opinion) groups/approaches to add:
Gambini Porto Pulliin Discrete space time
Connes Noncommutative geometry
Best
Jim Graber

 

[marcus]

Christine this is a selective outline, and in part subjective, where
I leave out many respectable nonstring QG researchers pursuing a variety of lines of research.
What I've indicated here are places where I currently see something interesting going on
or that I want to watch because of their near-term potential.

My subjective assessment (not based on citation counts or any sociology factors, but on the intrinsic merit) is that Ita's work is a lot of papers that don't go much of anywhere and are not part of the main developments in the field.

However you might not agree. I don't expect you necessarily to share my subjective view. So I will take a look at citation counts at this point:

http://www.slac.stanford.edu/spires/find/hep/www?rawcmd=FIND+EA+%22ITA%2C+EYO+EYO%2C+III%22&FORMAT=www&SEQUENCE=citecount%28d%29

12 papers, how many citations besides cases of the author citing himself? Essentially no sign that the work is of interest to the professional community. Maybe it's too early to say anything (first Ita papers appeared March 2007) but also too early to justify inclusion in a short list.

You could make your own list, Christine, as indeed you have done sometimes before! I have benefited from your perspective on QG research in the past very much. So if you have your own outline sketch of how it looks to you at present, I hope you will give us a link to it.

 

[jimgraber]

I still remember the old subdivision into covariant and canonical quantization.
It would be a help to me to tie the new approaches into this old but widely used categorization. It might also help us find or remember other approaches not yet included.
Here are some excerpts from a recent review by Claus Kiefer which I pulled off the arXiv:

“
http://arxiv.org/abs/gr-qc/0508120
Quantum Gravity: General Introduction and Recent Developments
Claus Kiefer

Covariant approaches (perturbation
theory, effective theory, and path integrals) and canonical approaches (quantum geometrodynamics,
loop quantum gravity).


What are the main approaches?
• Quantum general relativity: The most straightforward attempt, both conceptually and historically, is
the application of ‘quantization rules’ to classical general relativity. One distinguishes
– Covariant approaches: These are approaches that employ four-dimensional covariance at some
stage of the formalism. Examples include perturbation theory, effective field theories, renormalization-
group approaches, and path integral methods.
– Canonical approaches: Here one makes use of a Hamiltonian formalism and identifies appropriate
canonical variables and conjugate momenta. Examples include quantum geometrodynamics
and loop quantum gravity.
• String theory: This is the main approach to construct a unifying quantum framework of all interactions.
The quantum aspect of the gravitational field only emerges in a certain limit in which the
different interactions can be distinguished.
• There are a couple of other attempts such as quantization of topology, or the theory of causal sets,
which I will not address in this short review.”


I will be traveling the next three or four days and may not be able to post responses.
Happy Thanksgiving to those in the USA.
Best to all.
Jim Graber

 

[marcus]

...What generally is the difference between the spinfoam and pre-spinfoam approaches to LQG, and do they actually represent different approaches or just a different formalism for describing the same things? ...

You asked a lot of good questions. Until recently the spinfoam approach had no Immirzi parameter and no result about the spectrum of the area operator (comparable to canonical LQG). It was not known if the two approaches were compatible.

this year has been a breakthru year for spinfoam and it seems that it does have the Immirzi parameter and discrete area spectrum. It seems to coincide where the two approaches overlap. But I wouldn't take that as a certainty or attribute a lot of significance because there is still more work to be done on the new spinfoam vertex. It is less than a year old!

I still think of the two as different. Spinfoam is a PATH INTEGRAL approach, sometimes called "sum over histories". You look at all the ways that spatial geometry A can evolve into spatial geometry B (initial and final geometry states) and assign amplitudes to each evolutionary path and add up. It's Feynmanic.

Pre-1998 LQG was a CANONICAL approach. There is no time-evolution in this approach per se, but in applications one may be able to derive time evolution. In canonical LQG, the Hamiltonian is not an evolution operator but is a CONSTRAINT condition that guarantees that the particular spatial geometry you have is one which both could have evolved by the eintstein equation and can evolve further. A particular spatial geometry state is OK (satisfies the constraint) if it is in the KERNEL of the Hamiltonian (i.e. it is a zero of the operator).

Arnowitt Deser Misner (ADM) developed the canonical treatment of classical GR. So canonical formalism is not some special LQG thing, it was a well-established method---one recognized way to do things in GR. At its inception around 1990 LQG took the canonical approach.
Just in case anybody wants, here are some Wiki links
http://en.wikipedia.org/wiki/ADM_formalism
http://en.wikipedia.org/wiki/Canonical_gravity
http://en.wikipedia.org/wiki/Ashtekar_variables

This meant that LQG researchers first worked out the kinematics, set up the Hilbert to describe the states of spatial geometry, and then circa 1996 they started working on the dynamics.
(As I see it, kinematics and dynamics are jargon in this context, because what is called dynamics does not really look very dynamical in this case. Indeed it looks rather static! In this case dynamics means to define the Hamiltonian constraint operator. This allows to identify states of spatial geometry which could have arisen physically and will continue to evolve---so that one state, although it appears static or "frozen" nevertheless contains the information of all past and all future. Describing a whole spacetime by how it looks on one spatial slice is valid---but it does not seem very dynamic in a naive sense.)

Shortly after 1996 people discovered problems defining the Hamiltonian constraint in LQG and they began to get impatient with the canonical approach! Some, like Thiemann, stuck with it and may have made it work. His new book has the word "canonical" in the title.
I have seen some favorable comment.

Majority shifted over to path integral (spinfoam) approach, starting around 1998.

A spinfoam is like a spinnetwork but with one more dimension. A spinnetwork describes the quantum state of SPATIAL geometry. It is a labeled graph with vertices and edges.

A spinfoam is a diagram of how spinnet A can evolve into spinnet B. It has 2-D pieces as well as vertices and edges. The 2D pieces fill in where a spinnet edge traveled thru time, so to speak.

If you draw spinnet A at the bottom of the page and, while changing it into spinnet B, drag it up the page in the time direction, and make a BLUR. then that blur is the spinfoam. You change spinnets by discrete moves, which eliminate vertices, add vertices, and reconnect neighbor vertices in different ways. These official changes correspond to specific geometric things that happen in the corresponding spinfoam blur.

The relation between evolving spinnets and spinfoams is superficially obvious and straightforward. The difference is in how one handles dynamics----that is, how do you calculate the amplitude of geometry changing in some specific way? In the spinfoam case, you calculate an amplitude at a vertex. In the canonical case you have a Hamiltonian constraint operator.

this is very sketchy, coin. I have typed this very fast and hope it is not too misleading or full of mistakes. I hope it gives some useful sense of what is the difference between canonical LQG and spinfoam path integral.

 

[ccdantas]

Christine this is a selective outline, and in part subjective, (...)
What I've indicated here are places where I currently see something interesting going on
or that I want to watch because of their near-term potential.
(...)
12 papers, how many citations besides cases of the author citing himself? Essentially no sign that the work is of interest to the professional community. (...)

Hi Marcus,

Thanks for pointing out some of the criteria you are using to build up the "map".

BTW, it was an "easier" time to keep track of the developments in LQG about 2 years ago than now! So I appreciate your efforts.

But my criteria would be different. My personal list would be based on the materials that *I* find intrinsically interesting; I tend to despise citation counts and/or number of papers... these are of course important criteria, but sometimes they carry sociology bias... So, yes, I look at those criteria of course, but do not allow myself to be overly impressed. For that reason Ita's work would be on my map, it seems elaborate and formal enough to make me interested on it, and I think there is value in there. But I understand your point of view.

Thanks,
Christine

 

[marcus]

My personal list would be based on the materials that *I* find intrinsically interesting...

Exactly
why do you imagine that i am any different?
Based on looking over his papers I guess I decided by April or May that for me
his work was not intrinsically interesting.
I had already excluded Ita's work from what i am interested in several months before I was forced by others to look at his citation counts.

Ita does not participate in where I see QG going.
Several people challenged this, so eventually (sometime around October IIRC) I had to check his citations. They confirmed what was already my perception. But still, I could easily be wrong.

you have a different vision of the field, in which Ita's work is important. You could be right (I like your opinions and perspective as a rule, but disagree in this case). The value of citation counts is that it introduces one modest objective element that we can both look at, into a discussion which is primarily between two personal subjective views of the world.

Perhaps Ita will deliver a paper in July at QG² and achieve acclaim---causing surprise for me, and for you perhaps a sense of satisfaction and confirmation.

The other person who is working on validating the Kodama state is Andy Randono. If you think Ita's work is important then you should probably also keep track of Randono.

 

[ccdantas]

Exactly
why do you imagine that i am any different?

No, it is just that the criteria that you use to consider a paper interesting differ from mine; of course most human beings do or try to do what interest *themselves*...

Based on looking over his papers I guess I decided by April or May that for me
his work was not intrinsically interesting.

Why?

Ita does not participate in where I see QG going.

Where is it going?

Perhaps Ita will deliver a paper in July at QG² and achieve acclaim---causing surprise for me, and for you perhaps a sense of satisfaction and confirmation.

No, I don't think that way (I mean-- my approach to life is different!). But whatever, I don't see anything in quantum gravity being anywhere close to "acclamation"; this is a very rapidly evolving field, but even so I am skeptic that we are close to a consistent quantum gravity theory.

I find Ita's work interesting because he addresses a controversial and what I consider an important issue in quantum gravity (the Kodama state, more properly, the generalized state, as worked out by Randono). Here is an excerpt from http://en.wikipedia.org/wiki/Loop_quantum_gravity#The_Kodama_state":

Recently, Andrew Randono has published two papers that cite Witten's paper,[16][17] and address these objections, by generalizing the Kodama state, with the conclusion that the Immirzi parameter, when generalized with a real value, fixed by matching with black hole entropy, describes parity violation in quantum gravity, and is CPT invariant, and is normalizable, and chiral, consistent with known observations of both gravity and quantum field theory. The physical inner product may resemble the MacDowell-Mansouri theory formulation of gravity. Eyo Eyo Ita has published papers that build on Randono's generalized Kodama state, and argue that a generalized Kodama state can be built that can couple to matter and the Hamiltonian constraint can reproduce the dynamics of general relativity, resulting in a finite, full quantum gravity.


The possible relation with MacDowell-Mansouri gravity seems also very interesting to me.

The other person who is working on validating the Kodama state is Andy Randono. If you think Ita's work is important then you should probably also keep track of Randono.

Right, thanks!

Christine

 

[marcus]

Where is it going?

You are asking about how I see it, of course. You have your own perspective.
Where I see the field going is exactly what I outlined in post #1.

I respect Gambini et al enormously, for instance. Many brilliant and original papers.
But they, like Thiemann, are trying to make canonical dynamics work.
Eventually that could pay off but the current momentum is very much with path integral approaches instead.

I see much new work on the path integral side, especially spinfoam. A lot of open questions to work on. A lot of potential. Expect more people to be working in it and more results. By contrast not much is happening on the canonical side---dynamics-wise.

correct me if I am wrong, Christine, but the Kodama state seems to me to belong to an earlier historical period and to be embedded in canonical LQG

If you want to know a little of my thinking behind the map I posted above, I see a shift in the direction of dynamical TOPOLOGY (away from dynamical geometry) with more and more the older spacetime geometry ideas EMERGING from d.o.f. that look like topology to me. Or at least like the primitive topology of combinatorics. The keyword here is MOVES. In much of the new research the basic d.o.f. seem to evolve by local moves (that reconnect neighbors differently, or change the number of vertices.)

this is getting away from conventional differential geometry.
=====================

another way the field is going is towards APPLIED QG related to cosmology and astrophysical observation.

 

[ccdantas]

Hi Marcus,

Right, the current momentum as you say seems to be path integral approaches. But I wouldn't give up on canonical LQG so fast... I mean, perhaps there must be a personal bias here: my background is much more in GR than quantum field theory (or particle physics), and path integral is a technique that I have learned only recently (I'm not really much expert on it). GR is a subject that I am much more comfortable, as well as constrained Hamiltonian systems. I think that is why I am somewhat attached to the canonical approach. Thanks for sharing your thoughts on this.

Christine

 

[marcus]

what you say is all to the good. there have to be people who are rooted in each one of the different viewpoints and with focused persistent interest
then everything eventually gets thoroughly explored

 

[ccdantas]

Yes, but learning about other approaches is also a healthy thing to do. The problem is the lack of time for this... Making a "map" like you are doing helps a lot, with the caveat that it is a personal view.

Christine

 

[ensabah6]

Marcus, I have to agree with Christine here,

Presently, no semiclassical limit recovering general relativity has been shown to exist.

If the Kodama state has a semiclassical limit recovering GR, then I would argue it is probably the most important line of research. With GR as its semiclassical limit, LQG is interesting speculation, not necessarily related to 3+1 GR.

It would be interesting to see both Randanomo and Eyo publish more papers on the Kodama mama that are peer reviewed and cited.

Eyos papers include suggestions on how to connect LQC minisuperspace with the full Kodama state.

2. arXiv:0710.2337 [ps, pdf, other]
Title: Physical states in canonically quantized, finite, 4 dimensional quantum gravity. Minisuperspace Asktekar--Klein--Gordon model
Authors: Eyo Eyo Ita
Comments: 23 pages (submitted to Class. Quant. Grav.)
Subjects: General Relativity and Quantum Cosmology (gr-qc)

Exactly
why do you imagine that i am any different?
Based on looking over his papers I guess I decided by April or May that for me
his work was not intrinsically interesting.
I had already excluded Ita's work from what i am interested in several months before I was forced by others to look at his citation counts.

Ita does not participate in where I see QG going.
Several people challenged this, so eventually (sometime around October IIRC) I had to check his citations. They confirmed what was already my perception. But still, I could easily be wrong.

you have a different vision of the field, in which Ita's work is important. You could be right (I like your opinions and perspective as a rule, but disagree in this case). The value of citation counts is that it introduces one modest objective element that we can both look at, into a discussion which is primarily between two personal subjective views of the world.

Perhaps Ita will deliver a paper in July at QG² and achieve acclaim---causing surprise for me, and for you perhaps a sense of satisfaction and confirmation.

The other person who is working on validating the Kodama state is Andy Randono. If you think Ita's work is important then you should probably also keep track of Randono.

 

[marcus]

I should add links to the rough outline map made earlier, in case anyone wants to look at recent surveys and status reports, where available. Hopefully this "nonstring QG map" will help us know what papers to expect during the next couple of months and what developments to be prepared for.

For me it also raises two questions: which of these approaches will merge, or interfere constructively with which others. And also how will this spectator's map compare with the real map, which we will see around 1 July 2008 when the international conference QG-squared gathers? QG²-2008 is being organized by John Barrett (U. Nottingham) with the help of folks such as Ashtekar, Rovelli, Smolin, Baez, Majid, Grosse, and I forget who else.
http://www.maths.nottingham.ac.uk/conferences/qgsquared-2008/

Shahn Majid and Harald Grosse are helping organize because NCG (noncommutative geometry, Alain Connes stuff) is emerging as an important part of the picture. Realizing the standard particles geometrically.

How the QG conference shapes up will be a reality check for this attempt at a map. In any case, I'll fill in some links.

A. Three main sectors of Loop-community work:

1. Marseille new vertex
suggested review = latest Rovelli et al (what I think will probably be QG paper of the year)
http://arxiv.org/abs/0711.0146
https://www.physicsforums.com/showthread.php?t=194651

2. Penn State cosmology
suggested review = Ashtekar's latest
new feature = Bojowald on big bang nucleosynthesis
http://arxiv.org/abs/0710.3565
https://www.physicsforums.com/showthread.php?t=194678
https://www.physicsforums.com/showthread.php?t=194994

3. Perimeter dynamic topology
both geometry and matter emerge from topology of fourvalent braid network states
these states evolve by local moves which change how neighbor vertices are connected.
No current review, but see recent papers by Smolin and Wan.
Work in preparation by Bilson-Thompson, Hackett, Kauffman
(look for "Sun-Jon-Louis" paper)
http://arxiv.org/abs/0710.1548
https://www.physicsforums.com/showthread.php?t=190053

B. Other approaches to watch (several have no minimal scale, in other words scale -> 0 )

1. Legoblock path integral
Loll's review just came out
(CDT let's the size of the blocks go to zero)
http://arxiv.org/abs/0711.0273
https://www.physicsforums.com/showthread.php?t=196244

2. Running couplings--going with the flow
Percacci's review, "Asymptotic Safety"
(Reuter-Percacci let the energy scale k go to infinity)
http://arxiv.org/abs/0709.3851

3. Hodge star gravity, where the Hodge dual replaces metric d.o.f.
Krasnov's review just came out "Non-metric gravity: a status report"
(see section 3 on Renormalizability)
http://arxiv.org/abs/0711.0697
https://www.physicsforums.com/showthread.php?t=158899

4. Garrett Lisi's E8 gravity+matter----representing geometry + matter with an E8 connection
http://arxiv.org/abs/0711.0770

C. Dark horses:

1. Pereira and Aldrovandi's deSitter GR---a bold idea that runs a severe risk of being falsified by TeV gammaray telescope data. A fairly complete P and A paper on deS GR just appeared. So we have an up-to-date account of the status of their theory. Now it's up to astronomers to confirm or refute.
http://arxiv.org/abs/0711.2274

2. Jesper Grimstrup LQG + NCG---another risky project: putting Connes standard particle model into LQG.
Last paper was in 2006. Hopefully something from Aastrup and Grimstrup before long.
http://arxiv.org/abs/hep-th/0601127

====================I'm leaving out lots that is of interest (Baez, Thiemann, Gambini, Pullin, Dittrich, Wise, Perez,...)
Hard to see the field in its entirety. This outline fails to emphasize the importance of numerical work (Loll's, Christensen's, and Rideout's groups, the last two mentioned employ supercomputers like the Beowolf cluster and Cactus...)

 

[marcus]

I should add some links for B2 Asymptotic Safety
A December 2007 paper by Saueressig and Machado
http://arxiv.org/abs/0712.0445
On the renormalization group flow of f(R)-gravity
Pedro F. Machado, Frank Saueressig
55 pages, 7 figures
(Submitted on 4 Dec 2007)

"We use the functional renormalization group equation for quantum gravity to construct a non-perturbative flow equation for modified gravity theories of the form
$$S = \int d^dx \sqrt{g} f(R)$$
Based on this equation we show that certain gravitational interactions monomials can be consistently decoupled from the renormalization group (RG) flow and reproduce recent results on the asymptotic safety conjecture. The non-perturbative RG flow of non-local extensions of the Einstein-Hilbert truncation including
$$\int d^dx \sqrt{g} \ln(R)$$ and $$\int d^dx \sqrt{g} R^{-n}$$
interactions is investigated in detail. The inclusion of such interactions resolves the infrared singularities plaguing the RG trajectories with positive cosmological constant in previous truncations. In particular, in some $$R^{-n}$$-truncations all physical trajectories emanate from a Non-Gaussian (UV) fixed point and are well-defined on all RG scales. The RG flow of the $$\ln(R)$$-truncation contains an infrared attractor which drives a positive cosmological constant to zero, thereby providing a dynamical explanation of the tiny value of Lambda observed today."

Some PF posts about Asymptotic Safety, which may have useful links to earlier work:
https://www.physicsforums.com/showthread.php?t=187046
https://www.physicsforums.com/showthread.php?t=187512
https://www.physicsforums.com/showthread.php?t=178572

 

[marcus]

How will this (revised) spectator's map compare with the real map, to appear around 1 July 2008 when the international conference QG²-2008 meets?
http://www.maths.nottingham.ac.uk/conferences/qgsquared-2008/

The previous outline has been simplified---two main divisions instead of three.

A. Five main sectors of non-string QG work:

1. Marseille new spinfoam vertex
suggested review = latest Rovelli et al (what I think will probably be QG paper of the year)
http://arxiv.org/abs/0711.0146
https://www.physicsforums.com/showthread.php?t=194651

2. Penn State cosmology
suggested review = Ashtekar's latest
new features = Bojowald on big bang nucleosynthesis, black hole models by Gambini Pullin Vandersloot Boehmer
http://arxiv.org/abs/0710.3565
https://www.physicsforums.com/showthread.php?t=194678
https://www.physicsforums.com/showthread.php?t=194994

3. Perimeter dynamic topology
Both geometry and matter emerge from topology of fourvalent braid network states
these states evolve by local moves which change how neighbor vertices are connected.
No current review, but see recent papers by Smolin and Wan.
Work in preparation by Sundance Bilson-Thompson, Jonathan Hackett, Louis Kauffman
(look for "Sun-Jon-Louis" paper)
http://arxiv.org/abs/0710.1548
https://www.physicsforums.com/showthread.php?t=190053

4. Utrecht Legoblock path integral
Loll's review just came out
http://arxiv.org/abs/0711.0273
https://www.physicsforums.com/showthread.php?t=196244

5. Mainz-Trieste-Utrecht going with the flow
Percacci's review, "Asymptotic Safety"
http://arxiv.org/abs/0709.3851
Frank Saueressig's most recent contribution
http://arxiv.org/abs/0712.0445

B. Other approaches to watch

1. Kirill Krasnov's Hodge star gravity, where the Hodge dual replaces metric d.o.f.
Krasnov's review just came out "Non-metric gravity: a status report"
(see section 3 on Renormalizability)
http://arxiv.org/abs/0711.0697
https://www.physicsforums.com/showthread.php?t=158899

2. Garrett Lisi's E8 gravity+matter----representing geometry + matter with an E8 connection
http://arxiv.org/abs/0711.0770

3. Pereira and Aldrovandi's deSitter GR---a bold idea that runs a severe risk of being falsified by TeV gammaray telescope data. A fairly complete P and A paper on deS GR just appeared. So we have an up-to-date account of the status of their theory. Now it's up to astronomers to confirm or refute.
http://arxiv.org/abs/0711.2274

4. Jesper Grimstrup's LQG + NCG---another risky project: putting Connes standard particle model into LQG.
Last paper was in 2006. Hopefully something from Aastrup and Grimstrup before long.
http://arxiv.org/abs/hep-th/0601127

====================I'm leaving out much that is of interest (Baez, Thiemann, Gambini, Pullin, Dittrich, Wise, Perez,...) and failing to emphasize the importance of numerical work (Loll's, Christensen's, and Rideout's groups, the last two mentioned employ supercomputers like the Beowolf cluster and Cactus...)

 

[marcus]

More on A4 "Utrecht Lego path integral"

http://arxiv.org/abs/0712.2485
Planckian Birth of the Quantum de Sitter Universe
J. Ambjorn, A. Gorlich, J. Jurkiewicz, R. Loll
10 pages, 3 figures
(Submitted on 17 Dec 2007)

"We show that the quantum universe emerging from a nonperturbative, Lorentzian sum-over-geometries can be described with high accuracy by a four-dimensional de Sitter spacetime. By a scaling analysis involving Newton's constant, we establish that the linear size of the quantum universes under study is in between 17 and 28 Planck lengths. Somewhat surprisingly, the measured quantum fluctuations around the de Sitter universe in this regime are to good approximation still describable semiclassically. The numerical evidence presented comes from a regularization of quantum gravity in terms of causal dynamical triangulations."

the size in Planck terms of the universes under study is determined by computer memory and processing time.
It is limited by the numbe of building blocks they can handle. currently the most blocks in the model is about a third of a million. I wish they would use a larger, faster computer and run universes with several million blocks. here is a bit from their introduction:

==quote Loll et al==
To show that the physical spacetime surrounding us can be derived from some fundamental, quantum-dynamical principle is one of the holy grails of theoretical physics. The fact that this goal has been eluding us for the better part of the last half century could be taken as an indication that we have not as yet gone far enough in postulating new, exotic ingredients and inventing radically new construction principles governing physics at the relevant, ultra-high Planckian energy scale. – In this letter, we add to previous evidence that such a conclusion may be premature.
==endquote==

In other words they have evidence that space can arise from a very simple model, without need for new exotic ingredients