MVP-Senior: second quarter papers by QG faculty

[marcus]

So much potentially important QG reserach appeared this quarter (April-June 2008) that for simplicity I have split the list in two. Papers solely by graduate students and postdocs (no faculty co-author) are discussed in another thread:
https://www.physicsforums.com/showthread.php?t=243004
In my opinion some of the work by junior people this quarter was as significant and innovative as that by faculty. So I urge you to check the other thread out.

Here we are considering papers where at least one author is faculty. Which of the following five papers do you think will prove most valuable, and have the greatest impact on future QG research? I have provided some descriptive comment in parentheses, or else quoted from the authors' abstract or introduction section of the text. Comment from other people would be welcome. How did you decide on your choice? What discussion would you like to hear before making your pick?

1. Florian Conrady, Laurent Freidel
http://arxiv.org/abs/0806.4640
Path integral representation of spin foam models of 4d gravity
"We give a unified description of all recent spin foam models introduced by Engle, Livine, Pereira and Rovelli (ELPR) and by Freidel and Krasnov (FK). We show that the FK models are, for all values of the Immirzi parameter, equivalent to path integrals of a discrete theory and we provide an explicit formula for the associated actions. We discuss the relation between the FK and ELPR models and also study the corresponding boundary states. For general Immirzi parameter, these are given by Alexandrov's and Livine's SO(4) projected states. For 0 <= gamma < 1, the states can be restricted to SU(2) spin networks."

2. Stephon H.S. Alexander, Gianluca Calcagni
http://arxiv.org/abs/0806.4382
Superconducting loop quantum gravity and the cosmological constant
"We argue that the cosmological constant is exponentially suppressed in a candidate ground state of loop quantum gravity as a nonperturbative effect of a holographic Fermi-liquid theory living on a two-dimensional spacetime. Ashtekar connection components, corresponding to degenerate gravitational configurations breaking large gauge invariance and CP symmetry, behave as composite fermions that condense as in Bardeen--Cooper--Schrieffer theory of superconductivity. Cooper pairs admit a description as wormholes on a de Sitter boundary."

3. Abhay Ashtekar, Edward Wilson-Ewing
http://arxiv.org/abs/0805.3511
The covariant entropy bound and loop quantum cosmology
(Proving the important covariant entropy bound in LQG is a major milestone. The original conjecture by Bousso actually fails near the singularity in classic cosmology. LQC supplies what is needed to validate it.)

4. Laurent Freidel
http://arxiv.org/abs/0804.0632
Reconstructing AdS/CFT
"What is AdS/CFT from the point of view of background independent quantum gravity?"

5. J. Ambjorn, K.N. Anagnostopoulos, R. Loll, I. Pushkina
http://arxiv.org/abs/0806.3506
Shaken, but not stirred - Potts model coupled to quantum gravity
"We investigate the critical behaviour of both matter and geometry of the three-state Potts model coupled to two-dimensional Lorentzian quantum gravity in the framework of causal dynamical triangulations. Contrary to what general arguments of the effects of disorder suggest, we find strong numerical evidence that the critical exponents of the matter are not changed under the influence of quantum fluctuations in the geometry, compared to their values on fixed, regular lattices. This lends further support to previous findings that quantum gravity models based on causal dynamical triangulations are in many ways better behaved than their Euclidean counterparts."

 

[marcus]

the Freidel/Conrady paper

When setting up the poll, my guess was that the Ashtekar results on the entropy bound would prove most significant, but the Freidel/Conrady paper looks like a close second.

Florian Conrady presented this work at the QG2 conference last week. Here is his abstract, which refers to some extra stuff beyond what I saw in the paper:

"Semiclassical analysis of spin foam models of 4d gravity

We show that the Riemannian spin foam models by Freidel and Krasnov (FK) and Engle, Pereira and Rovelli (EPR) are equivalent to path integrals and give an explicit formula for the associated actions. We also determine suitable boundary terms, so that the path integrals preserve compositions of cobordisms. For general Immirzi parameter, the boundary states are given by Alexandrov's and Livine's projected states for SU(2)xSU(2). We use this path integral representation to derive classical equations for the spin foam models. With the help of an ansatz, the equations for the connection can be solved exactly: in analogy to continuum first-order gravity, the solutions are given by a co-tetrad on the simplicial complex and by a Levi--Civita connection that is uniquely fixed by the co-tetrad. When evaluated on these solutions, the action of the FK model is equal to the Regge action."

For a long time it has been a major goal to develop a version of LQG for which one could show good semiclassical behavior. I'd be interested in knowing what anyone who follows QG thinks about this: does this FC paper put us closer to that goal. It seems to me that it does.

John Baez has stressed that any theory of quantum gravity should respect composition of cobordisms. A cobordism is a spacetime viewed as a path thru spatial geometries that gets you from space-state A to space-state B. It is an evolution of geometry A into geometry B.
A kind of morphing. (rigorously, it is a 4d manifold with boundary consisting of two 3D manifolds A and B, but one can think of it as a smooth morphing of one into the other).
Morally speaking, a cobordism is the analog of a path integral. And John Baez, in his Quantum Quandaries paper, sets up QG as a functor making that analogy precise.
The upshot is that the wise and virtuous should look at spacetime as an evolution path or cobordism and QG as a quantization of that---namely as a path integral where nature is trying all sorts of crazy paths but they average out to what we normally experience. And to make categorical sense you must be able to join cobordisms together in sequence---going by one path segment and then segue on to the next and the next.

So at the moment it appears Freidel and Conrady are acting in accordance with a higher mathematical destiny---which could be called the Categorical Imperative except that Emanuel Kant already used that phrase. Maybe categorical directive is better.

And they could be verging on a nice classical or semiclassical limit for the FK (Freidel Krasnov) spinfoam.

 

[marcus]

more thoughts on the Freidel-Conrady paper (and the followup in prep)

Now that the QG2 conference (30 June - 4 July) is over it is becoming a little more clear to me what probably was the most significant recent work reported at the conference and posted on arxiv during the past quarter.

I think, in fact, that Francesca is probably right in her prediction, and that my original choice was off the mark.

Now we should be keeping an eye out for the next Freidel-Conrady paper which they say is in preparation. The title is
Semiclassical analysis of spin foam models of 4D gravity
and this now means path-integral analysis, which is a whole new ball-game.

This title overlaps with the plenary talk given at QG2 by Freidel. See the list of 14 plenary talks:
http://www.maths.nottingham.ac.uk/r...etry_and_quantum_gravity_conference/speakers/
The construction and semi-classical limit of spin foam models for 4d gravity

This sounds like big news because deriving the semiclassical limit for spinfoam is a Holy Grail-type research goal. Presumably this is being done via the new path-integral formalism which Freidel-Conrady introduced.

I wasn't at the conference and didn't hear Freidel's talk so I do not know how far they have come with demonstrating the semiclassical limit. We will see.

As I mentioned in the previous post, Florian Conrady gave a talk in parallel session which has the same title as the work in preparation cited in 0806.4640. It would not be surprising if it turns out to have the same abstract as well. So here is my guess as to the title and abstract of Freidel-Conrady's forthcoming paper:

Semiclassical analysis of spin foam models of 4d gravity

"We show that the Riemannian spin foam models by Freidel and Krasnov (FK) and Engle, Pereira and Rovelli (EPR) are equivalent to path integrals and give an explicit formula for the associated actions. We also determine suitable boundary terms, so that the path integrals preserve compositions of cobordisms. For general Immirzi parameter, the boundary states are given by Alexandrov's and Livine's projected states for SU(2)xSU(2). We use this path integral representation to derive classical equations for the spin foam models. With the help of an ansatz, the equations for the connection can be solved exactly: in analogy to continuum first-order gravity, the solutions are given by a co-tetrad on the simplicial complex and by a Levi--Civita connection that is uniquely fixed by the co-tetrad. When evaluated on these solutions, the action of the FK model is equal to the Regge action."

Sounds to me like the paper on our poll (0806.4640) is likely to turn out to be the first in a series of direct hits.

 

[marcus]

Well I have been joined by two other brave souls. Francesca and MTd2.
So now we have three picks: Freidel et al, Ashtekar et al, and Ambjorn et al.

Let's see if we can tell anything about how things are going. Normally it takes a while after a paper is posted on arxiv for citations to start building up because other researchers have to first read and understand the paper----then it influences their own research---finally they post new work citing the paper.

However, something that looks very good for Francesca's pick is that the Freidel-Conrady paper already has 1 citation---and it is a paper by two very well-known and active people: Bianca Dittrich and James Ryan.

Here is the Freidel-Conrady cits link
http://arxiv.org/cits/0806.4640
and it points to this
http://arxiv.org/abs/0807.2806
Phase space descriptions for simplicial 4d geometries
Bianca Dittrich, James P. Ryan
(Submitted on 17 Jul 2008)

"Starting from the canonical phase space for discretised (4d) BF--theory, we implement a canonical version of the simplicity constraints and construct phase spaces for simplicial geometries. Our construction allows us to study the connection between different versions of Regge calculus and approaches using connection variables, such as loop quantum gravity. We find that on a fixed triangulation the (gauge invariant) phase space associated to loop quantum gravity is genuinely larger than the one for length and even area Regge calculus. Rather, it corresponds to the phase space of area--angle Regge calculus, as defined by Dittrich and Speziale in [arXiv:0802.0864] (prior to the imposition of gluing constraints, that ensure the metricity of the triangulation). We argue that this is due to the fact that the simplicity constraints are not fully implemented in canonical loop quantum gravity. Finally, we show that for a subclass of triangulations one can construct first class Hamiltonian and Diffeomorphism constraints leading to flat 4d space--times."

The basic physical underlay here a CONVERGENCE of quantum gravity approaches. The Triangulation approach (Ambjorn-Loll et al) has achieved a PATH INTEGRAL or sum over quntum spacetime histories, from which deSitter space emerges, and an interesting result about the scaledependence of dimensionality. Part of the importance of the Freidel-Conrady paper is that it develops a spinfoam path integral which tends to bring LQG spinfoam closer to Triangulations, and make it look more like it can do the same things.

Or,what is also important, getting closer makes it possible to COMPARE approaches and see where they differ. Then this can give ideas about how to change one or the other approach.

Now already just one month after Freidel-Conrady posted, along comes Dittrich-Ryan and it has the same general thrust of bringing another QG approach closer to Triangulations (i.e. Simplicial) approaches---and comparing. Both Freidel and Dittrich are at Perimeter. Dittrich has co-authored with Loll. Here are lists of papers to give an idea of the authors' interests

http://arxiv.org/find/gr-qc/1/au:+Dittrich_B/0/1/0/all/0/1
http://arxiv.org/find/gr-qc/1/au:+Ryan_J/0/1/0/all/0/1
============================

So I guess the bottom line is that Francesca is doing OK poll-wise and there are solid physical reasons for it.

Her pick made a good start, getting already one citation in the first month. And it has to do with the fact that several QG approches are making rapid progress at the moment and there is a research effort to bring them alongside each other so they can be compared.

Other people might have a different take, which would be interesting to hear. Another aspect is that Freidel wants to show LQG spinfoam has the correct semiclassical limit and one means to do this is via Regge calculus. And recall this from the Freidel-Conrady abstract: "When evaluated on these solutions, the action of the FK model is equal to the Regge action."
And Regge is simplicial. So all this interest in Simplicial, and Path Integral, is not just convergence with the Triangulations approach. It may also be (and even primarily) a push for the semiclassical limit.

===============
Thanks to Francesca and MTd2 for joining the forecast poll. It makes it a lot more interesting. Registering a prediction involves taking a risk, and it is hard to see ahead. But it gets one thinking. I'd be glad to hear from others about what they think.

 

[marcus]

Heisenberg has joined us, so as of now four brave souls have hazarded predictions as to which of these will prove to be the second quarter MVP (most valuable paper). Something unusual happened---in this field you rarely see a paper's citations take off and fly in the first couple of months.

It can take 6 months to a year before several other researchers get ideas inspired by a paper and develop results derived from it and actually reach the point of posting something that cites it. So if a paper is going to be heavily cited, you may not know until a year after it comes out.

But it didn't even take 2 months for the Conrady Freidel to get 3 cites. Basically Francesca told us to key an eye on it. So I decided to post the cite links for each paper for convenience, making it easy to check anytime you like. The second link is to the cites.

1. Florian Conrady, Laurent Freidel
http://arxiv.org/abs/0806.4640
http://arxiv.org/cits/0806.4640
Path integral representation of spin foam models of 4d gravity

2. Stephon H.S. Alexander, Gianluca Calcagni
http://arxiv.org/abs/0806.4382
http://arxiv.org/cits/0806.4382
Superconducting loop quantum gravity and the cosmological constant

3. Abhay Ashtekar, Edward Wilson-Ewing
http://arxiv.org/abs/0805.3511
http://arxiv.org/cits/0805.3511
The covariant entropy bound and loop quantum cosmology

4. Laurent Freidel
http://arxiv.org/abs/0804.0632
http://arxiv.org/cits/0804.0632
Reconstructing AdS/CFT

5. J. Ambjorn, K.N. Anagnostopoulos, R. Loll, I. Pushkina
http://arxiv.org/abs/0806.3506
http://arxiv.org/cits/0806.3506
Shaken, but not stirred - Potts model coupled to quantum gravity

Previous posts in this thread have some discussion of the Conrady Freidel paper and also what I expect will be the abstract of the next Conrady Freidel paper to appear
Semiclassical analysis of spin foam models of 4d gravity (in preparation)

 

[marcus]

The poll has been growing. Christine Dantas has joined us, so we are now five people registering forecasts.
Christine and Francesca agree as to which paper will prove the most valuable to research in coming years.

Actually I suspect they are right, but one does not change one's prediction otherwise it would be no fun.

Checking the cites links, I see that the CF paper has 3 (from other notable people, not the authors citing their own work)
The rest have no cites or only one---that being a self-citation in one case. So even though it is early days the CF paper has already some distinction.what really counts though, as I see it, is the fact that it could change the formal basis of the spinfoam approach to a path integral defined more like that of CDT---over piecewise linear manifolds (geometries of glued 4-simplices). I could very easily be wrong, but what I see is a possible radical convergence and simplification of approaches.

It would be very interesting to hear some comment by Christine and/or Francesca as to why they picked that one. We should keep checking the Egregium blog in case Dantas posts about the paper there.
http://egregium.wordpress.com/

 

[ccdantas]

Hi Marcus,

I am somewhat following the progress of Freidel's papers, and I appreciate the meticulous developments of some necessary technical issues concerning how to introduce background independence into field theories; this is something fundamental towards quantum gravity. (In addition, his work in pure Yang-Mills is interesting on its own, from the standpoint of mathematical physics, I'd say, so I am biased to vote on him.) I didn't read about his paper on AdS/CFT, so I cannot vote on this one.

 

[ccdantas]

BTW I don't have much information on Florian Conrady, but a quick search has shown previous work on lattice Yang-Mills theory.

 

[marcus]

BTW I don't have much information on Florian Conrady...

I will try to help. But I don't either---basically none except the usual barebones facts----his PhD advisor was Carlo Rovelli. PhD 2005 Uni Berlin. Apparently in the european system you can be a PhD student at Berlin and have Rovelli as your thesis supervisor. Akademische Reisefreiheit.
(probably the academic travel-freedom tradition goes back to Middle Ages

After PhD he postdoc'd at Penn State with Ashtekar 2005-2006 and then I think Perimeter as of sometime 2007-2008 presumably working with Freidel at Perimeter. Max Planck Potsdam always as a second home. Seriously outstanding guy, just looking at publications as a grad student back to 2002
http://www.perimeterinstitute.ca/index.php?option=com_content&task=view&id=30&Itemid=72&pi=6045
http://www.perimeterinstitute.ca/en/Scientific/Research/Quantum_Gravity/

 

[marcus]

Hey Christine! You picked a winner! I just looked at cites for the Freidel-Conrady paper and already FOUR after being posted only a couple of months

 

[marcus]

This is a question to either or both Christine and Francesca. I think there are definite physics reasons why the F-C paper is outstanding. What got your attention?

What physics did you see in the F-C paper (By F-C could stand for the Francesca-Christine choice, but I mean Freidel-Conrady ) that made you pick that one.

For me, I didn't see right away, but now I would say that being able to go to the DUAL of a spinfoam and look at the corresponding simplicial complex---a piecewise linear manifold---and actually write out the action for the dual path-integral. For me this looks like a kind of break-out---creating more freedom. It's one reason I like it.