# Two best QG papers so far this quarter-other ideas?

1. May 6, 2008

### marcus

Two best QG papers so far this quarter--other ideas?

Part of doing regular QG NEWS AND OVERVIEW has been having a poll every three months to get people's views on the papers appearing that quarter which they think will be most important for future research----a Most Valuable Paper (MVP) forecast poll.

We are now roughly halfway through the quarter (April-June) and I'm starting to collect nominations---for a short list of candidates for most field-changing paper.

I've seen TWO that in my view are obvious choices so far.

One of them links Triangulation QG with no-extra-dimension String.
The other makes a major advance in discovering braid-matter in QG networks---particles as complications in the state of geometry represented by the evolving LQG network.

Background on the Triangulations QG paper
Technical terms are "Causal Dynamical Triangulations" (CDT) and "non-critical String theory".
Non-critical String can include cases where the spacetime dimension is 2, 3 or 4. The CDT people typically get their results by starting off with the easy 2d case and working up to 3d and 4d. They can simulate the appearance and evolution of quantum universes in the computer---approximated using large numbers of 4d triangles called simplexes. Using these simplex building blocks is why it's called "triangulations".

The paper is by 5 people: based in Denmark, Holland, Iceland, Japan and the UK. Their names are Ambjorn, Loll, Westra, Watabiki, and Zohren.
http://arxiv.org/abs/0804.0252

Bear in mind that for them String is a little different from what you might be used to. The string IS the universe. In the 2d case they begin by studying, the universe is spatially a circle, one space dimension. The worldsheet is two-dimensional and it represents spacetime.

Background on the braid-matter paper

The braid matter paper is by Song He (Beijing University) and Yidun Wan (Perimeter Institute). http://arxiv.org/abs/0805.0453

I intend to give a light non-technical overview of what is going on with these papers, and also to give, either in this thread or in a separate one, a largescale MAP of QG activities at present. I'd welcome comments of course. If you wish, have a look at the two papers which I'm nominating for this quarter's best-of-lot and contribute some views and explication

2. May 6, 2008

### marcus

One necessity for communicating QG news and overview is that most people don't have a MAP of the field in mind. It is a fast-moving changing field with a number of different approaches. Studying an isolated paper doesn't work without providing context.

There are various ways to sketch out a map of the main approaches to QG, one way is to use the names of leading PEOPLE as symbols of the main research lines. This gives too much importance to individuals, but it is easy to remember. Saying ROVELLI here does not mean only Carlo Rovelli. It means all the other people that have been contributing to the kind of thing he does (Etera Livine, Laurent Freidel, Jon Engle, Kirill Krasnov, Simone Speziale, and many many others, far too many to try to list.)

Rovelli and others have been joining the loop and foam approaches. These have been developing separately for about 10 years. The loop approach has made most progress in QG kinematics while foam has dealt with dynamics. In the past two years Rovelli and other have merged the two approaches and found a surprising compatibility---they really seem now to be the same theory! Recently Rovelli has shown a new interest in moving over into Quantum Cosmology and bridging the gap between the main LQG theory (loopfoam?) and the reduced Loop Quantum Cosmology (LQC) theory which is a simplification specialized to cosmology.

Ashtekar and others have been focusing on LQC, which is the main theory APPLIED to cosmology. In the past couple of years they have developed computer models that can be started before the big bang and, after a contraction and bounce, reproduce behavior expected from conventional cosmology models. Martin Bojowald has also been a leader in Loop Cosmology. Analytical solvable models have been developed as well as numerical computer models.

Cosmology is much simpler than the full QG theory, because the description of the universe is boiled down to a few important parameters. In simplifying from LQG to LQC some provisional choices are made, and assumptions like homogeneity. Effort is now beginning to focus on gradually removing the simplifying assumptions and bridging the disconnect between LQG and LQC.

Loll and others have developed Causal Dynamical Triangulations in the past 10 years. Remarkable progress has come in the past 3 years. Spacetime is approximated by a huge number of simplexes (a "triangulation") which assemble themselves according to simple local rules. The result is a path integral of dynamically evolving geometry. There are analytical versions of CDT in two dimensions and the 3 and 4 dimensional versions run in the form of computer simulations. Random universes are generated in the computer and studied. There have been some striking results including the observation of reduced dimensionality at microscopic scale and the tendency of the path integral to average out to a deSitter universe at large scale. The cosmological constant plays a crucial role in CDT. Researchers are based in various places like Tokyo, London, Copenhagen, Reykjavik, but the main center for CDT work is Utrecht, Holland.

Reuter and others have an approach often referred to as Asymptotic Safety. One of the chief researchers in that line is Roberto Percacci, who is now at Utrecht. The Asymptotic Safety group has also found evidence of a reduction of spatial and spacetime dimensionality at microscopic scale---a kind of fractal-like structure emerges at very small scale. I expect some collective effort involving both CDT and Asymptotic Safety because they both have shown similar results about the microscopic structure of spacetime.

Smolin and others have been developing various ways to do braid-matter. The essential thing here is that you take the usual way that LQG has always represented the quantum state of spatial geometry---the network. This network (the quantum state of geometry) evolves, according to local moves that add remove and reconnect vertices.
You take this network and you find patterns of twistings and criscrossings in it.
So these are microscopic COMPLICATIONS OF GEOMETRY and you find that these little quirks in the geometry can propagate and combine and interact with each other. So then you CLASSIFY these little quirky patterns in the microgeometry, and see if you get groups that resemble those of the known particles.

Then the dynamics of local moves (the "dual Pachner moves" by which the network evolves) comes to govern not only the dynamics of conventional geometry but also the dynamics of the braids---which might or might not turn out to be matter. It is a high risk program because it easily might not turn out.

Barrett and others are putting together QG with Noncommutative Geometry. John Barrett was co-author of the longest standing spinfoam model---the prevalent one used in LQG for much of the past 10 years. He recently got a NCG result simultaneously with Alain Connes---a result about realizing the particle Standard Model with NCG. Barrett is organizing a conference scheduled for early July called QG2 or Quantum Geometry and Quantum Gravity. A lot of people are working on how to put QG together with QG.

Ali Chamseddine a frequent co-author with Alain Connes will be giving a talk at Barrett's QG2 conference. The talks are about half from the LQG side (e.g. Carlo Rovelli) and half from the NCG side (e.g. Chamseddine.)

So that is the map that gives some context for seeing what this quarter's most valuable papers are. They should be innovative papers, making notable advances, and they should do that in context of the larger picture of what is going on in Quantum Gravity.

I have to go out for now, but I will get back and talk some more about these two individual papers that I'm suggesting are the best so far this quarter. If you have comments on these, or others to propose, feel free.

3. May 6, 2008

Wrong forum?

4. May 6, 2008

### Gokul43201

Staff Emeritus
If this thread is going to be about the scientific merit (methodology for judging "best") of the papers, it belongs in BtSM.

5. May 6, 2008

### marcus

I'm a science watcher---more specifically a physics watcher. I do News and Overview.

I rarely get down to the equations in a paper, but as a retired mathematician I can usually do what of that I need to when I need it.

Gokul,
AFAIK there is no METHODOLOGY for predicting which papers will be most valuable to future research, most influential/fruitful. most likely to have a field-changing significance.

I take a holistic view of this. Individual papers are part of the larger picture. The larger picture, especially in quantum gravity, is changing dynamically. Personally I am looking for papers that take risks and point out new directions. Of course that is just my particular approach.

If there is a place for News and Overview of new fundamental physics, if this forum is the place, and it wont offend anyone here, then this thread had better stay peacefully here.
In my humble opinion.

In the past I've organized quarterly MVP polls as forecast polls. We don't pretend to know or discover the truth, we predict which papers will have impact. Later you can look back and see if who, if anyone, was right in the provisional sense of their choice spawning a bunch of later research. People show the extent to which they understand the present by how often they guess right about the future.

Last edited: May 6, 2008
6. May 6, 2008

### marcus

Hi mheslep,
I have good associations with you, don't remember why. Maybe you took part in a forecast poll or some other thread I was in.
The main objective measure of how much impact a paper has on some line of research is CITATION COUNTS. the landmark papers tend to be the highly cited ones. Of course subjective judgment matters too. There is no recipe, human intuition and balance is key.
But the objective business of peer-review publication and cites is certainly an important part.

So I am going to be counting citations. And publications. Not only that, but that is part of it.

I don't want other people to be offended by this and attack it. I don't want the distraction of having to argue about meeting this or that person's preconceptions of this or that forum. I want a quiet place where I can do new fundamental physics News and Overview, spot trends, and people who want to can read it, other people simply ignore it. So maybe because counting citations is a part of Physics Watching it turns out that Physics Watching belongs in Sociology. This is fine.

7. May 8, 2008

### josh1

What kind of mathematician we're you?

8. May 8, 2008

### Moonbear

Staff Emeritus
I think we can raise the bar and discuss the actual science within the articles as part of the discussion of what merits a good paper on the subject. Counting citations is not always an ideal method of determining impact...a single lab with a lot of publications may cite their own works many times while nobody else is, or someone who presents a flawed paper may get cited often as others provide rebuttals or conflicting findings. Within the context of the science forums here, let's have people discuss the actual science...a critical review of a few well-chosen papers could be a great learning opportunity here.

9. May 8, 2008

### Staff: Mentor

Marcus posted this in Social Science, a mentor moved it here.

10. May 13, 2008

### marcus

That is a good suggestion! Beginning in 2004 I've devoted many pages of writing in several different threads to explaining the science content in the CDT papers of Renate Loll. Describing how her model works and trying to make it intuitive. I could get links to some earlier PF threads about Loll's approach, as well as to the papers which we have discussed. It would be delightful if folks want to discuss (or re-discuss) Causal Dynamical Triangulations.

As for braid-matter, less has been written. I think one way to get some of the basics is to watch Yidun Wan's video lectures. I gave the links in a recent braid-matter thread. The format is split screen, so you see Yidun talking at the blackboard on one screen and see the current slide he is using on the other screen. Please let me know, anybody, if you try these seminar talks and have difficulty of some kind with them.

11. May 13, 2008

### JustinLevy

I watched the talks you linked to. I also skimmed the paper. Unfortunately my knowledge is not good enough to address my first take on this:
It is neat to see that they got a different 'dimension' to emerge for spacetime on short and large scales. But the fact that they got 4d spacetime to emerge seems a bit cheating when they started with 4d simplexes. Yes, by taking the limit that the size of the simplexes goes to zero we can ignore some details of embedding, but it still seems to me that they in some sense chose the answer they wanted to start with.

Am I missing something? Or is that an active area (seeing if the emergent spacetime is independent of the choice of fundemental building block)?

Even so, it is still interesting to see that on short scales the universe may appear to only have one spatial dimension (which implies on short scales the strength of 'forces' go from 1/r^2 to becoming independent of distance... a kind of 'asymptotic freedom' for any elementary force?).

12. May 13, 2008

### marcus

Yes and it is partly my fault. I didn't give you any link to a CDT paper explaining the basics---how dimension is defined and measured. Why it was a highly nontrivial result when they finally got 4D spacetime coming out.

The whole process took about 10 years---starting with low dimension (2D spacetime) and working up. In dynamical triagulations when triangles are assembled (glued along the edges) randomly you don't necessarily get a 2D result at large scale. In the early 1990s pathologies were noticed---the dimension could get arbitrarily large, essentially become infinite. Or it could come out too small---around 1 instead of desired 2D.

In 1998, Loll and Ambjorn got some insight and tried something that worked in 2D. Then the question was, would it work in 3D? So they developed the tools and gradually extended the result. Finally in 2004 they got the thing working in 4D.

So it doesn't automatically come out. You take 4-simplex building blocks and have them assemble into random geometries (governed by the discrete Regge version of the Einstein Hilbert action), and it is highly nontrivial for the overall largescale geometry to be 4D.

In fact at small scale the dimensionality at any given point is a quantum observable which typically comes out non-integer and much less than 4. The scale at which you measure the dimensionality of the space is important.

The important picture to have in mind is that a spacetime is like a Feynman path integral where a particle goes along all possible paths to get from A to B. And the paths are nowhere differentiable with probability one. The paths are very jagged. It is the same with an Ambjorn Loll space time. It is a path in "geometry space" getting from initial geomety A to final geometry B. Each possible path is VERY UNSMOOTH.

Think about how you would measure the dimensionality at a point at a certain scale in a totally unsmooth space. It is not like in conventional differential geometry. You might for example plot radius against volume (socalled Hausdorff definition of dimensionality) or you might run a random walk and see how fast the walker gets lost (spectral dimension).

Anyway Ambjorn Loll can attach AMPLITUDES to these spacetimes or paths in geometry space, and do observations and average, and compute quantum observables. And they can actually do the sum over all paths (in their simplex regularization) by Monte Carlo means and get what the overall path integral is. This came out December 2007. It is fascinating. A lot of interesting stuff is coming out.

If you Google Renate Loll and go to her website she has links to all the papers---recent ones and also tutorial-type ones that cover the basics. If you want, I will suggest some that I've found helpful.

Anyway its is not cheating When you start with triangles you dont necessarily get largescale 2D, when you start with tetrahedra you don't always get largescale 3D and so on.
the dimensionality can crash or blow up. quite a lot of research papers about this from before 1998.

13. May 13, 2008

### MTd2

Why getting 4 dimensions out of 4 simplexes is NOT obvious?

14. May 13, 2008

### marcus

think of it in the 2D case, to make it easy for yourself.
imagine that you are gluing together triangles along their edges (that is the 2D analog of gluing together 4 simplices along their tetrahedral sides)

think about how you are going to define the dimensionality of the result at some chosen point

one of the simplest definitions of dimensionality (where the space is not smooth) is just to see how volume grows as a function of radius. Hausdorff.

Radius is the number of steps from triangle to triangle you can take.
Volume is the number of triangles you can contact, in a given number of steps.

If the volume grows as the SQUARE of the number of steps you take out from the point, then the Haus. dim. is two.

But it is easy to imagine gluing 50 triangles together along their edges so they ALL can be contacted within one step---so the dimensionality is 50, not 2
====================

this illustrates, in lower dimension, one of the pathologies encountered in the early 1990s by people trying to develop dynamical triangulations as a quatum theory of gravity.

15. May 14, 2008

### marcus

well, not 50, some large number >> 2
==============

one problem people could be having is thinking of a 2D simplicial complex (a collage of triangles) as embedded in ordinary 3D Euclidean. If you think of it all happening in familiar surroundings, then you will get hung up. The idea is you have a bunch of identical triangles---you can think of them as all equilateral. You can glue as many of them as you want around a point.

that is not true if they are restricted to lie in a plane. You can only glue 6. Like pie slices.
If it is not restricted to be planar, but still has to exist in 3D Euclid space, you have a bit more liberty. You can glue as few as 3, and you can imagine doing more than 6 by various tricks like a ruffled collar, or a fanfold. But it is still pretty restrictive.

But if there is no such restriction at all, no embedding in some fixed surrounding, that opens up a lot more possbilities.
==============

Anyway the key idea is that Loll QG is like a Feynman path integral where any given spacetime is a kinky path thru a world of kinky 3D geometries. The "sum over histories" is regularized, made finite, by building everything out of identical building blocks---which you then let the size go to zero. Long day today and it's bedtime. Maybe someone else will take over explaining CDT, or I will do some more tomorrow.

Last edited: May 14, 2008
16. May 23, 2008

### marcus

We are still accumulating nominations for MVP (most valuable paper) of this quarter (April-June 2008) and another one showed up that is pretty clearly important

]http://arxiv.org/abs/0805.3511
The covariant entropy bound and loop quantum cosmology
Abhay Ashtekar, Edward Wilson-Ewing
15 pages, 3 figures
(Submitted on 22 May 2008)

"We examine Bousso's covariant entropy bound conjecture in the context of radiation filled, spatially flat, Friedmann-Robertson-Walker models. The bound is violated near the big bang. However, the hope has been that quantum gravity effects would intervene and protect it. Loop quantum cosmology provides a near ideal setting for investigating this issue. For, on the one hand, quantum geometry effects resolve the singularity and, on the other hand, the wave function is sharply peaked at a quantum corrected but smooth geometry which can supply the structure needed to test the bound. We find that the bound is respected. We suggest that the bound need not be an essential ingredient for a quantum gravity theory but may emerge from it under suitable circumstances."

The point is that the entropy bound is a CONJECTURE which you can't prove starting from other QG theories. It is a big deal so people were thinking it should be put into QG theories as an axiom, that is to say by hand. They should be constructed to satisfy the bound and one of their basic ingredients.

What Ashtekar etal suggest is that in the Loop case you get it for free. You dont have to build it into the theory as an ingredient because you probably can derive it as a consequence.

That's big news. It's probably an important paper. So we should include it in the MVP poll and maybe we can have a discussion thread, if people are interested.

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

I want to review the list of what we have so far. Possible MVP candidates. This one by Loll et al is interesting because it links up Triangulations (CDT) with string/M

http://arxiv.org/abs/0804.0252
A Matrix Model for 2D Quantum Gravity defined by Causal Dynamical Triangulations
J. Ambjorn, R. Loll, Y. Watabiki, W. Westra, S. Zohren
13 pages, 1 figure
(Submitted on 1 Apr 2008)

"A novel continuum theory of two-dimensional quantum gravity, based on a version of Causal Dynamical Triangulations which incorporates topology change, has recently been formulated as a genuine string field theory in zero-dimensional target space (arXiv:0802.0719). Here we show that the Dyson-Schwinger equations of this string field theory are reproduced by a cubic matrix model. This matrix model also appears in the so-called Dijkgraaf-Vafa correspondence if the superpotential there is required to be renormalizable. In the spirit of this model, as well as the original large-N expansion by 't Hooft, we need no special double-scaling limit involving a fine tuning of coupling constants to obtain the continuum quantum-gravitational theory. Our result also implies a matrix model representation of the original, strictly causal quantum gravity model."

And there were these two by Song He and Yidun Wan that came out this quarter

http://arxiv.org/abs/0805.0453
Conserved Quantities and the Algebra of Braid Excitations in Quantum Gravity
Song He, Yidun Wan
25 pages, 2 figures
(Submitted on 5 May 2008)

"We derive conservation laws from interactions of braid-like excitations of embedded framed spin networks in Quantum Gravity. We also demonstrate that the set of stable braid-like excitations form a noncommutative algebra under braid interaction, in which the set of actively-interacting braids is a subalgebra."

http://arxiv.org/abs/0805.1265
C, P, and T of Braid Excitations in Quantum Gravity
Song He, Yidun Wan
28 pages, 5 figures
(Submitted on 9 May 2008)

"We study the discrete transformations of four-valent braid excitations of framed spin networks embedded in a topological three-manifold. We show that four-valent braids allow seven and only seven discrete transformations. These transformations can be uniquely mapped to C, P, T, and their products. Each CPT multiplet of actively-interacting braids is found to be uniquely characterized by a non-negative integer. Finally, braid interactions turn out to be invariant under C, P, and T."

These aren't the only possible candidates but they are some. There was also one by Laurent Freidel which might be interesting because it links up the Spinfoam approach to QG with the AdS/CFT conjecture

http://arxiv.org/abs/0804.0632
Laurent Freidel
34 pages
(Submitted on 4 Apr 2008)

"In this note we clarify the dictionary between pure quantum gravity on the bulk in the presence of a cosmological constant and a CFT on the boundary. We show for instance that there is a general correspondence between quantum gravity radial states'' and a pair of CFT's. Restricting to one CFT is argued to correspond to states possessing an asymptotic infinity. This point of view allows us to address the problem of reconstructing the bulk from the boundary. And in the second part of this paper we present an explicit formula which gives, from the partition function of any 2 dimensional conformal field theory, a wave functional solution to the 3-dimensional Wheeler-DeWitt equation. This establishes at the quantum level a precise dictionary between 2d CFT and pure gravity."

Last edited: May 23, 2008
17. Jun 3, 2008

### marcus

Here is another to add to the list for this quarter

http://arxiv.org/abs/0805.4696
Regularization and finiteness of the Lorentzian LQG vertices
Jonathan Engle, Roberto Pereira
13 pages
(Submitted on 30 May 2008)

"We give an explicit form for the Lorentzian vertices recently introduced for possibly defining the dynamics of loop quantum gravity. As a result of so doing, a natural regularization of the vertices is found and suggested. The regularized vertices are then proven to be finite."
====================================

It's hard to guess the future importance of new research papers. I would be glad of other people's comments on these. The time period April May June is only 2/3 over and we already have some 5 candidates. Here's the list so far:

1. Jonathan Engle, Roberto Pereira
Regularization and finiteness of the Lorentzian LQG vertices
(the new spinfoam vertex formula is an important development, this paper pushes ahead with it and that could count for a lot)

2. Abhay Ashtekar, Edward Wilson-Ewing
The covariant entropy bound and loop quantum cosmology
(proving the cov. entropy bound in LQG, important bound, major landmark, the original conjecture by Bousso fails in classic cosmology at the singularity and so proving it actually requires the quantum version)

Then there's a pair of papers by
3. Song He, Yidun Wan
Conserved Quantities and the Algebra of Braid Excitations in Quantum Gravity

C, P, and T of Braid Excitations in Quantum Gravity
(hard to judge, is this really a way for matter to enter into the background independent quantum gravity?)

And something that could easily prove the most important, by
4. Laurent Freidel