What is the recent development of Loop Quantum Gravity

[marcus]

Some interesting recent developments in LQG.

http://arxiv.org/abs/1201.2187
A spin-foam vertex amplitude with the correct semiclassical limit
Jonathan Engle
(Submitted on 10 Jan 2012)
Spin-foam models are hoped to provide a dynamics for loop quantum gravity. All 4-d spin-foam models of gravity start from the Plebanski formulation, in which gravity is recovered from a topological field theory, BF theory, by the imposition of constraints, which, however, select not only the gravitational sector, but also unphysical sectors. We show that this is the root cause for terms beyond the required Feynman-prescribed exponential of i times the action in the semiclassical limit of the EPRL spin-foam vertex. By quantizing a condition isolating the gravitational sector, we modify the EPRL vertex, yielding what we call the proper EPRL vertex amplitude. This provides at last a vertex amplitude for loop quantum gravity with the correct semiclassical limit.
4 pages

see also Alesci Rovelli's proposal for new Hamiltonian:
Google "alesci rovelli hamiltonian arxiv" and get http://arxiv.org/abs/1005.0817

and the Freidel Geiller Ziprick paper:
Google "freidel geiller ziprick" and get http://arxiv.org/abs/1110.4833

More discussion here:
https://www.physicsforums.com/showthread.php?p=3637688#post3637688
https://www.physicsforums.com/showthread.php?p=3643430#post3643430
https://www.physicsforums.com/showthread.php?p=3624456#post3624456

 

[tom.stoer]

In order not to confuse the reader:

A "proper vertex amplitude" to recover the correct semicalssical limit is a necessary but not a sufficient condition for the model to be "correct". Of course one must recover GR as low energy theory, but in the deep QG regime there may very well be a whole bunch of inequivalent theories with the same semiclassical limit.

This is the main reason why some people insist on
1) a completion of the canonical formulation (constructing a "correct" H) plus
2) a consistent quantization in terms of spin foams plus
3) a proof of equivalence of (1) and (2)

All three pathways are being investigated, but up to now neither completion of 1) or 2) nor convergence in the sense of 3) can be claimed.

@marcus: did you spent some time in looking into the 2011 Thiemann papers? There are some interesting aspects like going beyond dim=4 and incorporating SUSY.

 

[marcus]

Another recent development. The cosmological constant Λ put into spinfoam cosmology and one gets a nontrivial solution to the Einstein equation out: de Sitter space.

It's kind of beautiful. The Friedmann equation with cosmo constant is derived from the Zakopane spinfoam amplitude (with Λ inserted). And this turns out to be compatible with the treatment where Lambda is a quantum group deformation parameter. Several things brought together in one paper.

Google "bianchi krajewski spinfoam cosmology" and get
http://arxiv.org/abs/1101.4049
Cosmological constant in spinfoam cosmology
Eugenio Bianchi, Thomas Krajewski, Carlo Rovelli, Francesca Vidotto
(Submitted on 20 Jan 2011)
We consider a simple modification of the amplitude defining the dynamics of loop quantum gravity, corresponding to the introduction of the cosmological constant, and possibly related to the SL(2,C)q extension of the theory recently considered by Fairbairn-Meusburger and Han. We show that in the context of spinfoam cosmology, this modification yields the de Sitter cosmological solution.
4 pages, 2 figures

for the treatment where Λ appears in quantum group, related to the q-deformation, see papers by Muxin Han and by Fairbairn Meusberger. It's fascinating that in that treatment one would expect that Λ running to large values (as in asym safe gravity) with high energy density corresponds to a decline in angular resolution---angles get fuzzy things are either in the same direction or they are not, lacking fine angular distinctions. It's intriguing.
But one does not have to deal with the quantum group idea of how Λ arises. One can simply insert it in the Zakopane spinfoam amplitude---or in the Friedmann equation---and treat it as a constant the way cosmologists customarily do.

this paper was a "sleeper". I'm not sure we recognized its importance back in the first quarter of 2011.

 

[marcus]

Tom, raised an interesting point in the Shapo-Wetter thread, which this paper could serve as partially answering.

I think it's amazing that such an enormous work and resulting profound insights can perhaps (!) be traced back to a wrong assumption ;-) That does not necessarily mean that the reults are wrong, of course

It would be interesting to find a close relationship between AS and LQG.

I saw some recent results on AS applied to Holst action with different results as for Einstein-Hilbert. This is striking.

The cosmological constant is treated differently in both approaches; in LQG one tries to incorporate it already when defining the algebraic foundations as a q-deformation of SU(2); in AS it behaves as a standard running coupling 'constant'; these two ideas seem to be incompatible at a very fundamental level.

What the Bianchi Krajewski et al paper suggests to me is that the two ideas (which Tom points out SEEM to be incompatible) are not actually incompatible.

You can see from 1101.4049 equation (2) that in LQG the cosmological constant can indeed be treated as a "standard running coupling", as it is in the Asymptotic Safe approach.

And it can also be treated as a q-deformation of SL(2,C) as per Han, Meusberger, Fairbairn and others. The paper tentatively suggests the two ways of including Λ are "possibly related"!

 

[marcus]

Since it may be possible to MERGE Asym Safe QG with Loop QG (and get something that works better than AS currently does at the cosmo singularity) I want to pay close attention to recent AS talks and papers. Here is the abstract for Frank Saueressig's 15 February video lecture:

Google "saueressig pirsa fractal" and get
http://pirsa.org/12020088/
Fractal Space-times Under the Microscope: a RG View on Monte Carlo Data
Frank Saueressig
The emergence of fractal features in the microscopic structure of space-time is a common theme in many approaches to quantum gravity. In particular the spectral dimension, which measures the return probability of a fictitious diffusion process on space-time, provides a valuable probe which is easily accessible both in the continuum functional renormalization group and discrete Monte Carlo simulations of the gravitational action. In this talk, I will give a detailed exposition of the fractal properties associated with the effective space-times of asymptotically safe Quantum Einstein Gravity (QEG). Comparing these continuum results to three-dimensional Monte Carlo simulations, we demonstrate that the resulting spectral dimensions are in very good agreement. This comparison also provides a natural explanation for the apparent conflicts between the short distance behavior of the spectral dimension reported from Causal Dynamical Triangulations (CDT), Euclidean Dynamical Triangulations (EDT), and Asymptotic Safety.
Date: 15/02/2012 - 4:00 pm

and also recall the Bianchi et al paper from 2 posts back:

Google "bianchi krajewski spinfoam cosmology" and get
http://arxiv.org/abs/1101.4049
Cosmological constant in spinfoam cosmology
Eugenio Bianchi, Thomas Krajewski, Carlo Rovelli, Francesca Vidotto
(Submitted on 20 Jan 2011)
We consider a simple modification of the amplitude defining the dynamics of loop quantum gravity, corresponding to the introduction of the cosmological constant, and possibly related to the SL(2,C)q extension of the theory recently considered by Fairbairn-Meusburger and Han. We show that in the context of spinfoam cosmology, this modification yields the de Sitter cosmological solution.
4 pages, 2 figures

They derive the Friedman equation for deSitter space starting from the Zakopane dynamics equation with a λ term inserted for cosmo constant.

 

[marcus]

Several interesting parallels between AsymSafe QG and Loop are appearing. One is an explanation of dark matter as clouds of small black holes. We see this from Modesto in the Loop case and from Easson in the Safe QG case. Modesto has been working on this for several years---I'll get a recent paper of his with Hossenfelder and you can check the references.
Google "modesto emission spectra" and get http://arxiv.org/abs/1202.0412
Emission spectra of self-dual black holes
Sabine Hossenfelder, Leonardo Modesto, Isabeau Prémont-Schwarz
(Submitted on 2 Feb 2012)
We calculate the particle spectra of evaporating self-dual black holes that are potential dark matter candidates. We first estimate the relevant mass and temperature range and find that the masses are below the Planck mass, and the temperature of the black holes is small compared to their mass. In this limit, we then derive the number-density of the primary emission particles, and, by studying the wave-equation of a scalar field in the background metric of the black hole, show that we can use the low energy approximation for the greybody factors. We finally arrive at the expression for the spectrum of secondary particle emission from a dark matter halo constituted of self-dual black holes.
15 pages, 6 figures,

Small conventional BH don't last long since they get hotter as they lose mass and evaportion speeds up. By contrast, small Loop BH last a very long time since they get colder as they lose mass.

Curiously enough Easson has come up with a similar conclusion in the Safe QG case.
Google "easson safe black hole" and get http://arxiv.org/abs/1007.1317
Black holes in an asymptotically safe gravity theory with higher derivatives
Yi-Fu Cai, Damien A. Easson
(Submitted on 8 Jul 2010)
We present a class of spherically symmetric vacuum solutions to an asymptotically safe theory of gravity containing high-derivative terms. We find quantum corrected Schwarzschild-(anti)-de Sitter solutions with running gravitational coupling parameters. The evolution of the couplings is determined by their corresponding renormalization group flow equations. These black holes exhibit properties of a classical Schwarzschild solution at large length scales. At the center, the metric factor remains smooth but the curvature singularity, while softened by the quantum corrections, persists. The solutions have an outer event horizon and an inner Cauchy horizon which equate when the physical mass decreases to a critical value. Super-extremal solutions with masses below the critical value correspond to naked singularities. The Hawking temperature of the black hole vanishes when the physical mass reaches the critical value. Hence, the black holes in the asymptotically safe gravitational theory never completely evaporate. For appropriate values of the parameters such stable black hole remnants make excellent dark matter candidates.
22 pages, 3 figures; version to appear in JCAP



==links to some recent papers==
New Hamiltonian:
Google "arxiv alesci rovelli hamiltonian" and get http://arxiv.org/abs/1005.0817

Intro, Survey, Tutorial, Open Problems for Research:
Google "ashtekar introduction 2012" and get http://arxiv.org/abs/1201.4598
Google "rovelli zakopane" and get http://arxiv.org/abs/1102.3660

Cosmological Constant:
Google "bianchi cosmic constant spinfoam" and get http://arxiv.org/abs/1101.4049
Google "pawlowski cosmic constant" and get http://arxiv.org/abs/1112.0360

Loop Classical Gravity--the right version of GR to quantize:
Google "freidel geiller ziprick" and get http://arxiv.org/abs/1110.4833
Google "jonathan ziprick pirsa" and get http://pirsa.org/12020096

Small black holes and dark matter:
Google "modesto emission spectra" and get http://arxiv.org/abs/1202.0412
Google "easson safe black hole" and get http://arxiv.org/abs/1007.1317

Miscellaneous:
Google "freidel speziale BF" and get http://arxiv.org/abs/1201.4247 [ways to get GR from BF]
Google "wise symmetry gravity" and get http://arxiv.org/abs/1112.2390 [different approach to hamiltonian]

 

[torsten]

Thanks marcus for the recent overview and thanks tom for the very interesting discussion.

Like Tom, I also have some trouble with LQG. Especially I think some of the problems came form the lack of understanding the 'local-global' problems (or sometimes mix them).
But no one considers the relation (and the special features) between 3 and 4 dimensions.
After the breakthrough of Perelman, we know that the relation between homogenous gemetries in 3 dimensions and 3-manifold topology is very close.
A general 3-manifold consist of a mix of 8 possible gemetries (related to the Bianchi model I to IX). This close relation is the reason that the Einstein-Hilbert action in 3 dimensions is a topological invaraint (Chern-Simons invaraint).
The situation changes dramatically in 4 dimensions. The relation between geometry and topology is lost but there is a new one between the smoothness structure (the maximal smooth atlas) and the topology.
This new relation is essential for the understanding of the dynamics: the sum over 3-geometries will automatically lead to the inclusion of pathes like:
spherical 3-geometry -> hyperbolic 3-geometry -> spherical 3-geometry
The corresponding 4-manifold can have the topology [math]S^3\times R[/math] but an exotic smoothness structure (I considered this case in http://arxiv.org/abs/1201.3787 )

This fact has also an impact on spin foam models. Usually one try to relate thise models to a triangulation of the 4-manifold. But smoothness structures and piecewise-linear structures (as a kind of triangulations) are equivalent.
Therefore oen has something like an exotic triangulation.
To address these questions, one has to consider the class of topspin models (Marcolli, Dustopn et. al.) using branched coverings. In this approach one sees the problem:
every 3-manifold can be obtained by a 3-fold covering of the 3-sphere branched along a 1-dimensional complex, a knot or link, and
every 4-manifold can be obtained by a 4-fold covering of the 4-sphere branched along a 2-dimensional complex, a surface, but the surface contains 2 singularities: the cusp and the fold.
The appearance of cusp singularities was already discussed in the spin foam literature as conical singularities.

I agree with marcus and tom, that the Alesci/Rovelli hamiltonian is a real breakthrough, it considers a more global change of spacetime.

So again thanks for the overview, I will go more deep into these new papers.

Torsten

 

[marcus]

Hi Torsten!
You could give some general words on what you expect first and foremost from a QG theory, to provide a context.

For me the basic requirement is a clear testable one that reproduces classical geometry (where applicable) and resolves the cosmo singularity.

That's what I want from QG first and foremost, and then if there are several QG theories successful in this basic way then I will ask which one follows Dirac quantization plan most transparently, which one has both hamiltonian and path integral versions most clearly equivalent and so on.

Because if you have more than one theory that works, these niceties can be useful in selecting from among them.

But right now i do not see a multitude of QG theories that meet the basic requirements.
As for Loop, I see steady progress, a growing understanding of how to set up the classical phase space, quantize it, and get a hamiltonian version, mounting evidence that classical GR is recovered, that the cosmological singularity is resolved, and that it is testable. Numerous papers on all these fronts.

So I *expect* a hamiltonian version to be constructed that will be equivalent to the Zako spinfoam version or whatever it has evolved into by that time. The present formulation is remarkably clear and simple so it is hard to imagine how it could change, but it could of course.

But my basic desiderata are not that (unless there are several equally good theories to choose from). My requirements, as I said, are a clearly formulated testable theory which reproduces classical GR where valid and can model the start of expansion---forming the basis for cosmology.

I'm curious about what you would say instead of this. You are actively engaged in your own QG program. You must have some basic goals, primary objectives. You may have summed up your philosophy in one or more of your papers and can just give a page/paragraph reference or paste something in here. Or maybe it is something you can say informally in just a few words.

 

[tom.stoer]

Like Tom, I also have some trouble with LQG. Especially I think some of the problems came form the lack of understanding the 'local-global' problems (or sometimes mix them).

Thanks Torsten; it's is comforting when an expert identifies similar issues.

The situation changes dramatically in 4 dimensions. The relation between geometry and topology is lost but there is a new one between the smoothness structure (the maximal smooth atlas) and the topology. ... This fact has also an impact on spin foam models. Usually one try to relate thise models to a triangulation of the 4-manifold. But smoothness structures and piecewise-linear structures ... are equivalent.

It's clear that this must be your perspective ;-) but I agree, problems regarding PL and smoothness structures have been overlooked (or ignored) in the LQG community for a long time.

Here I have one central question: what is the fundamental structure of (L)QG:
1) PL or smooth manifolds with diffeomorphisms factored away - resuting in triangulations?
2) generic spin networks?

Not all generic spin networks are dual to some triangulation (of a manifold), and therefore there are spin networks for which no triangulation of a manifold does exist (at least the dimension of the manifold can be rather large).

... every 4-manifold can be obtained by a 4-fold covering of the 4-sphere branched along a 2-dimensional complex, a surface, but the surface contains 2 singularities: the cusp and the fold.

This results in another central question: in (L)QG, do we have to use a 3-dim. or a 4-dim manifold to start with?

My impression is that the SF models rely in some sense on some fundamental structures of the underlying 4-manifold, whereas the generic spin networks do have no such limitations. It's interesting that spin networks arise from manifolds with rather severe restrictions (3-space foliations of globally hyperbolic 4-manifolds, local diffeomorphisms, i.e. no singularites) but that once the construction is completed they seem to be agnostic regarding these restrictions.

So spin networks are a much richer structure than triangulations.

 

[marcus]

Interesting comments, Tom, I hope Torsten will discuss some of your questions. About your central question you know there are different formulations, and some do use 3D and 4D manifolds. "Do we have to?" It seems not since not every formulation of the theory does. The version I am most familiar with does not have these structures embedded. It uses both spin networks and spinfoams but they are not immersed in any continuum.

You are totally correct that "not all generic spin networks" are dual to triangulations! For one thing a spin network is not restricted to having just 4-valent nodes (which would correspond to tetrahedra in the dual). It's normal to have nodes with valence > 4 corresponding (fuzzily, indefinitely) to many-sided polyhedral chunks of space.

 

[tom.stoer]

marcus, there may very well be n-valent nodes which do not correspond to triangulations but which may describe Voronoi-cell-like structures; but I think that not even this structure need always be sufficient. I am afraid that an arbitrary graph need not comply with any cell-like structure embedded in low-dimensional manifolds.

 

[marcus]

I am afraid that an arbitrary graph need not comply with any cell-like structure embedded in low-dimensional manifolds.

Is that important?
I was responding to your talking about triangulations. The overwhelming majority of graphs, of any given size, are NOT dual to a triangulation. So I wanted to agree with emphasis!

I think you can probably extend that to a division of a 3D manifold into 3D cells which are NOT simplices. Is this the kind of thing you mean? Most graphs would not be dual to that sort of structure either. Or so I believe (haven't thought about it.)

I was puzzled by your saying you are afraid such and such might not be so. Don't see why it matters.

 

[marcus]

Since the topic of polyhedra has come up, I'll mention some recent work in that area:
http://arxiv.org/abs/1009.3402 (google "bianchi polyhedra")
Polyhedra in loop quantum gravity
Eugenio Bianchi, Pietro Dona', Simone Speziale
32 pages

As it happens, I see that Eugenio Bianchi is at UC Berkeley this week giving a couple of talks. He has a co-author in the physics department so maybe they are working on something. Anyway there is this paper about quantum polyhedra. A quantum polyhedron (state space a space of intertwiners) can be thought of as a blur of possible classic polyhedra. Volume may be specified, also number of sides and areas. But shapes of sides may be indeterminate.

A quantum state of geometry might be imagined as a collection of quantum polyhedra, with adjacency relations. You aren't guaranteed the ability to match the faces.

The loop literature does not say something naive like space IS a bunch of quantum polyhedra, that is just one way to think about the theory. There are various ways of approaching and visualizing that give intuition. Use them if they help you but don't get hung up on them.

Another way, also worked out primarily by Eugenio, is to think of it as a quantum theory of topological defects. All the geometry, the curvature etc, is concentrated on the cracks and crevasses between chunks, which are flat (everything is flat except at the defects where they meet.)

This also is a way to visualize LQG, a guantum theory of the defects between otherwise flat chunks of space. The Freidel Geiller Ziprick paper takes off from Bianchi's work on this and, as you probably recall, develops it further.
http://arxiv.org/abs/0907.4388 (google "bianchi aharonov")
Loop Quantum Gravity a la Aharonov-Bohm
Eugenio Bianchi
19 pages

 

[torsten]

Hi Marcus, hi Tom,

my original goal of the last post was to say thank you for the good discussion.
But to meet the goal of this thread, here are some general remarks or better my motivation:

Also for me the basic requirement is a clear testable version of QG that reproduces classical geometry (where applicable) and resolves the cosmo singularity.
(like you Marcus) But more must be possible: an explainantion of dark matter / energy and inflation.
Currently, LQG is one of the best candidates to meet all these criteria.

So, from the QG point of view I'm rather a 'LQG follower'. But that don't prevent me from a critique of some aspects of the current research, like Tom does.
I never start my own QG program. I started with the investigaton of 4-dimensional smooth manifolds to understand general aspects of dynamics.
Currently there is a lot of work to find the Hamiltonian via trial and error (my opinion). So I miss a general concept for the next steps.
The large number of workers on that field is a great advantage.

My own philosophy is a little bit different: I agree to produce a testable version reproducing known theories in some limits.
Since 20 years ago I learn in my first topology lecture at the university of the existence of exotic R^4. So immediatly I wa interested.
What is the relevance of exotic smoothness for physics? The first results came from Carl Brans (I met him in 1995). Then we are both occupied with the book project.
The idea was very simple: two referenece systems (or systems of charts, i.e. an atlas) are equivalent if both a diffeomorphic to each other.
But then two non-equivalent reference systems (representing different physics) are non-diffeomorphic. In 4 dimensions it can be indepedent of the topology.
Therefore exotic spacetimes can be seen as different physical systems (of a spacetime with fixed topology).
My own investigations began around 1995 (when I thought to have studied enough differential topology) but with classical relativity theory by showing that exotic smoothness can be the source of a gravitational field.
Nearly 10 years later we found the first relation to quantum mechanics by constructing a factor II_1 von Neumann algebra (the Fock space of a fermion). You maybe remember on the discussion in 2005 in this forum.
There are only very few people working in this field. A student of M. Marcolli, Christopher Duston, joined our community and began to calculate the Euclidean path integral for different exotic smoothness structures.
It was folklore that exotic smoothness contributes (or better dominates) the path integral but no one showed it. Chris was the first to tackle this problem by perturbatively calculate it.
His results inspired me to calculate also the Lorentz case. In two papers we calculate (non-perturbatively) the exotic smothness part to show area quantization as a result (confirming LQG).
In parallel we try to find another description of exotic R^4's (without infinite handlebodies) and end with an amazing relation to codiemnsion-1 foliations. This relation brought us back to think about QG.
The space of leafs of a foliation was one of the first examples of a non-commutative space and geometry by Connes. In case of our foliation we obatin a factor III_1 von Neumann algebra also known as observablen algebra of a QFT (in the algebraic sense).
Currently we also find relations to Connes-Kreimer renormalization theory and to the Tree QFT of Rivasseau (arXiv:0807.4122).

But enough about history, my real motivation for this work is the relation between geometry and physics. Especially the question, what is quantum geometry? The simple answer, the quantization of the spacetime, is not correct.
(I will have a lookinto Bianchis polytop theory soon.)
So from the philosophical point of view, I'm interested in the relation between geometry and quantum theory, especially which one is the primary principle. Because of exotic smoothness, I believe it is geometry.
But then I have to understand the measurement process etc also from a geoemtrical point view. Another driving force is the naturalness, i.e. to derive the expressions for the Dirac action, the standard model etc. from geometrical expressions.
This brings me back to your discussion here. I miss the guiding principle in the current constructions in LQG. Of course there are excepts (Freidel is one, sometimes Rovelli). Everyone speaks about unification but currently there are alwyas two entities: the spin network and the dynamical spacetime (or the string and the background).
A real unification should end with one entity.


But now to your interesting questions:
what is the fundamental structure of (L)QG:
1) PL or smooth manifolds with diffeomorphisms factored away - resuting in triangulations?
2) generic spin networks?

As I tell in my previous post, I'm impressed by Marcollis topspin model. Then the spin network (as 1-dimensional complex) produces the 3-manifold as branched cover. Then we have one entity (the network) producing the space.
The spin network (as the expression of holonomies) has a topological interpretation: every closed loop in the network must be corespond to one element of the fundamental group of the 3-manifold. After the solution of Poincare conjecture we know that the fundamental group characterizes a 3-manifold uniquely.
Therefore (in my opinion) the two cases 1) and 2) are more connected then anybody thought.

The second question: in (L)QG, do we have to use a 3-dim. or a 4-dim manifold to start with?
is much harder to comment.
Usually one starts with a globally hyperbolic 4-manifold (SxR, S Cauchy surface) and one has to discuss only the topology of the Cauchy surface. Otherwise later one speaks about fluctuating geometries (by quantum fluctuations) which can be result in a topology change (at the Planck level).
But a topology change destroys the global hyperbolicity (now naked singularities appear). So, at first one has to discuss the global hyperbolicity condition. Even in the exotic smoothness case one lost this condition (see http://arxiv.org/abs/1201.6070).
But did we really need it? The main reason for its introduction were causility question. But now we know (after some work of Dowker about causal continuity) that topology change is possible.
Naked singularities seem bad at the first view but we need them (to prevent the horror of Parmenides block universe, i.e. a complete determinism). Such a singularity separates the past from the future. Then we cannot completely determine the trajectory of a particle
That is for me a necessary condition to implement quantum mechanics.
Therefore for my opinion, one should start with a spacetime (4dim) and should look for codim 1 subspaces (the 3dim space).

 

[marcus]

Thanks Torsten, this is one of the most thoughtful and interesting posts in my experience here at the BTSM forum! I appreciate your care in laying out your thoughts on QG and different smooth structures.

I just heard a 90 minute presentation at the UC physics department by Eugenio Bianchi which had some suggestive parallels with your research focus. He was talking about the dynamics of topological defects (as an alternative formulation of Loop gravity.)

There were questions and discussion during and after so it took the full two hours. Steve Carlip participated quite a lot. Good talk.

The slides overlapped some with those in the PIRSA video which you can watch if you wish:
Google "pirsa bianchi" and get http://pirsa.org/11090125/

PIRSA:11090125
Loop Gravity as the Dynamics of Topological Defects
Speaker(s): Eugenio Bianchi
Abstract: A charged particle can detect the presence of a magnetic field confined into a solenoid. The strength of the effect depends only on the phase shift experienced by the particle's wave function, as dictated by the Wilson loop of the Maxwell connection around the solenoid. In this seminar I'll show that Loop Gravity has a structure analogous to the one relevant in the Aharonov-Bohm effect described above: it is a quantum theory of connections with curvature vanishing everywhere, except on a 1d network of topological defects. Loop states measure the flux of the gravitational magnetic field through a defect line. A feature of this reformulation is that the space of states of Loop Gravity can be derived from an ordinary QFT quantization of a classical diffeomorphism-invariant theory defined on a manifold. I'll discuss the role quantum geometry operators play in this picture, and the perspective of formulating the Spin Foam dynamics as the local interaction of topological defects.
Date: 21/09/2011

As I say, many of the slides are the same as those of today's talk, but there seem to be new results, and I got more out of it the second time---either today's presentation contained more intuition and insight or else the questions by Carlip and Littlejohn helped bring out stuff. Anyway great!

I can't help suspecting that there is some kinship between the dynamics of topological defects and your investigation of differential structures.

One obvious difference from the September PIRSA talk was that this came after the October Freidel Geiller Ziprick paper in effect laying out a "constrain first then quantize" approach, developing the "Loop Classical Gravity" concept. There were several references to FGZ http://arxiv.org/abs/1110.4833 .

 

[marcus]

Looking over the schedule of the April meeting of the American Physical Society, one sees that there will be an invited talk reviewing current research in Spinfoam and Loop QG
http://meetings.aps.org/Meeting/APR12/Event/170161
Eugenio Bianchi (Perimeter Institute)
Loop Quantum Gravity, Spin Foams, and gravitons
Loop Quantum Gravity provides a candidate description for the quantum degrees of freedom of gravity at the Planck scale. In this talk, I review recent progress in formulating its covariant dynamics in terms of Spin Foams. In particular, I discuss the main assumptions behind this approach, its relation with classical General Relativity, and its low-energy description in terms of an effective quantum field theory of gravitons.

The session of invited QG talks is chaired by Jorge Pullin, who also chairs the regular session
"Quantum Aspects of Gravitation"
http://meetings.aps.org/Meeting/APR12/SessionIndex2/?SessionEventID=172413

Here are a few of the talks scheduled for the regular QG session.

http://meetings.aps.org/Meeting/APR12/Event/170104
Hal Haggard (UC Berkeley)
Volume dynamics and quantum gravity
Polyhedral grains of space can be given a dynamical structure. In recent work it was shown that Bohr-Sommerfeld quantization of the volume of a tetrahedral grain of space results in a spectrum in excellent agreement with loop gravity. Here we present preliminary investigations of the volume of a 5-faced convex polyhedron. We give for the first time a constructive method for finding these polyhedra given their face areas and normals to the faces and find an explicit formula for the volume. In particular, we are interested in discovering whether the evolution generated by this volume is chaotic or integrable which has important consequences for loop gravity: If the classical volume generates a chaotic flow then the corresponding quantum spectrum will generically be non-degenerate and the volume eigenvalue continues to act as a good label for spin network states. On the other hand, if the volume flow is classically integrable then the degeneracy of the corresponding quantum spectrum will have to be lifted by another observable. We report on progress distinguishing these two cases. Either of these outcomes will impact the direction of future research into volume operators in quantum gravity.

http://meetings.aps.org/Meeting/APR12/Event/170098
Rodolfo Gambini, Nestor Alvarez, Jorge Pullin (Montevideo, LSU)
A local Hamiltonian for spherically symmetric gravity coupled to a scalar field
Using Ashtekar's new variables we present a gauge fixing that achieves the longstanding goal of making gravity coupled to a scalar field in spherical symmetry endowed with a local Hamiltonian. It opens the possibility of direct quantization for a system that can accommodate black hole evaporation. The gauge fixing can be applied to other systems as well.
[my comment: related paper= http://arxiv.org/abs/1111.4962 ]

http://meetings.aps.org/Meeting/APR12/Event/170100
Jacopo Diaz-Polo, Aurelien Barrau, Thomas Cailleteau, Xiangyu Cao, Julien Grain (LSU, CRNS Paris)
Probing loop quantum gravity with evaporating black holes
Our goal is to show that the observation of evaporating black holes should allow the standard Hawking behavior to be distinguished from Loop Quantum Gravity (LQG) expectations. We present a Monte Carlo simulation of the evaporation of microscopic black holes in LQG and perform statistical tests that discriminate between competing models. We conclude that the discreteness of the area in LQG leads to characteristic features that qualify evaporating black holes as objects that could reveal specific quantum gravity footprints.
[my comment: related paper= http://arxiv.org/abs/1109.4239 ]

http://meetings.aps.org/Meeting/APR12/Event/170102
Seth Major (Hamilton College)
Coherent States and Quantum Geometry Phenomenology
The combinatorics of quantum geometry can raise the effective scale of the spatial geometry granularity predicted loop quantum gravity. However the sharply peaked properties of states built from SU(2) coherent states challenge the idea that such a combinatorial lever arm might lift the scale of spatial discreteness to an observationally accessible scale. For instance, the Livine-Speziale semi-coherent states exhibit no such lever arm. In this talk I discuss how an operational point of view suggests a different class of coherent states that are not built from states with microscopic classical geometry. These states are introduced, compared to previous coherent states, and the status of the combinatoric lever arm is discussed.

 

[torsten]

Thanks a lot for your words, Marcus
As usual, I like your recommendations. So I will have a look into Bianchi's article. The lecture is really interesting. It seems we share the same passion...
Maybe one thought which is independent of exotic smoothness:
In our article about topological D-branes
http://arxiv.org/abs/1105.1557
we discussed wild embeddings to use it as a quantum version of D branes.
An embedding is a map i:N->M so that i(N) is homeomorphic to N. The embedding is called tame if i(N) is represented by a finite polyhedron. Examples are Alexanders horned sphere or Antoines necklace. One of the main characteristica of a wild embedding is that the complement M\i(N) is mostly a non-simple connected space. Other examples of wild embeddings are also called fractals...
In section 5.3 we describe a wild embedding by using Connes non-commutative geometry, i.e. we associate a C* algebra to the wild embedding. All the resulst of this paper seem to imply that a quantum version of a D brane is a wild embedded D-brane. Maybe also any other quantum geometry is of this kind.
But now I will study your recommendations...

 

[tom.stoer]

torsten, I strongly believe that you miss one important point regarding your own work; it seems to me that (once you succeed with your program ;-) you will be able to explain why we live in a four-dim. spacetime!

 

[torsten]

Good point Tom, that was one of the reasons I began to study exotic smoothness. When I heard from this result, I studied superstring theory. But then I changed to differential topology to understand this result.

 

[marcus]

Yes good point: the multitude of structures does make D=4 special, or is one of the things that makes it special. Another thing to note is the suggestion of spontaneous dimensional reduction at extremely small scale which has appeared in several separate theory contexts as reviewed by Steve Carlip. BTW I forgot to mention another invited Loop talk at the April APS meeting.
There is a session called Advances in Quantum Gravity
consisting of three invited talks. One of the these, already mentioned, is by Eugenio Bianchi: a review of recent advances in Loop QG Spin Foams and gravitons. Abstract: http://meetings.aps.org/Meeting/APR12/Event/170161

I overlooked another Loop invited talk to be given by Ivan Agullo from Penn State:
http://meetings.aps.org/Meeting/APR12/Event/170160
Beyond the standard inflationary paradigm

The inflationary paradigm provides a compelling argument to account for the origin of the cosmic inhomogeneities that we observe in the CMB and galaxy distribution. In this talk we introduce a completion of the inflationary paradigm from a (loop) quantum gravity point of view, by addressing gravitational issues that have been open both for the background geometry and perturbations. These include a quantum gravity treatment of the Planck regime from which inflation arises, and a clarification of what the trans-Planckian problems are and what they are not. In addition, this approach provides examples of effects that may have observational implications, that may provide a window to test the basic quantum gravity principles employed here.

I hope to find something on arxiv that can give more of an idea what this will be about. I could not find anything the first try. It's late, have to look further tomorrow.

=======EDIT======
Well, I looked again this morning and couldn't find anything on arxiv that I could recognize as a clear indication of what this talk might be about. Ivan Agullo has worked a lot with Leonard Parker. He was at Parker's institution and is now with Ashtekar group at Penn State, I think. He brings a lot of non-Loop cosmology to Loop, or so it seems to me. I woujld like to see a paper co-authored by Agullo and Ashtekar, but I can't find one so far.

I will check ILQGS for a talk by Agullo.

Inflation is important because a some previous approaches to inflation bring on the multiverse ailment. You invent an inflaton field and then spend the rest of your life trying to make excuses for it.

 

[marcus]

Ah hah! I found a March 2011 ILQGS talk by Agullo
http://relativity.phys.lsu.edu/ilqgs/agullo032911.pdf
Observational signatures in LQC

He refers to work in progress by Ashtekar, William Nelson, and himself. This is precisely what is apparently not yet written up so I can't find on arxiv. It would be the basis of his invited presentation at the American Physical Society April meeting in Atlanta:

http://meetings.aps.org/Meeting/APR12/Event/170160
Beyond the standard inflationary paradigm
Ivan Agullo (Penn State)
... In this talk we introduce a completion of the inflationary paradigm from a (loop) quantum gravity point of view, by addressing gravitational issues that have been open both for the background geometry and perturbations. These include a quantum gravity treatment of the Planck regime from which inflation arises... In addition, this approach provides examples of effects that may have observational implications, that may provide a window to test the basic quantum gravity principles...


BTW today (28 February) the ILQGS will have a talk by Marc Geiller, one of the co-authors of the FGZ paper. This paper topped our fourth quarter MIP poll last year. It offers a new approach to constructing LQG as a "quantization" of a classical theory.

Google "ILQGS" and get http://relativity.phys.lsu.edu/ilqgs/

Scroll down to March 2011 to get links to audio and slides of Agullo's talk.

Geiller's talk about the FGZ research is currently at the top of the same page:
http://relativity.phys.lsu.edu/ilqgs/geiller022812.pdf
Continuous formulation of the loop quantum gravity phase space
He's at "Paris-Diderot": the Diderot campus of the University of Paris, on the right bank near the city's southeast edge.

 

[marcus]

Tomorrow 29 February the Perimeter QG group has talk by Wolfgang Wieland
which I hope will be online as video and slides. Postdocs at PI get to bring visitors to the Institute. I think Wolfgang is coming as Eugene Bianchi's guest. His home-base at this point is Marseille.
http://pirsa.org/12020129
Spinor Quantisation for Complex Ashtekar Variables
Wolfgang Wieland
Abstract: During the last couple of years Dupuis, Freidel, Livine, Speziale and Tambornino developed a twistorial formulation for loop quantum gravity.
Constructed from Ashtekar--Barbero variables, the formalism is restricted to SU(2) gauge transformations.
In this talk, I perform the generalisation to the full Lorentzian case, that is the group SL(2,C).
The phase space of SL(2,C) (i.e. complex or selfdual) Ashtekar variables on a spinnetwork graph is decomposed in terms of twistorial variables. To every link there are two twistors---one to each boundary point---attached. The formalism provides a clean derivation of the solution space of the reality conditions of loop quantum gravity.
Key features of the EPRL spinfoam model are perfectly recovered.
If there is still time, I'll sketch my current project concerning a twistorial path integral for spinfoam gravity as well.
29/02/2012 - 4:00 pm

Wieland's 29 February talk (available online at ILQGS) will evidently be based on this paper:
http://arxiv.org/abs/1107.5002
Twistorial phase space for complex Ashtekar variables
Wolfgang M. Wieland
(Submitted on 25 Jul 2011, last revised 24 Jan 2012)
We generalise the SU(2) spinor framework of twisted geometries developed by Dupuis, Freidel, Livine, Speziale and Tambornino to the Lorentzian case, that is the group SL(2,C). We show that the phase space for complex valued Ashtekar variables on a spinnetwork graph can be decomposed in terms of twistorial variables. To every link there are two twistors---one to each boundary point---attached. The formalism provides a new derivation of the solution space of the simplicity constraints of loop quantum gravity. Key properties of the EPRL spinfoam model are perfectly recovered.
18 pages, Classical and Quantum Gravity 29 (2012) 045007

 

[torsten]

Thanks marcus for your effort.
Yes inflation is indeed important. But one of the current problems is the infinity of the inflation process, i.e. if the inflation process (with the inflaton) is started then there is no known process which stops the inflation.
The second problem is agin the naturalness: there ar ean infinity of possibilities for the potential of the inflaton field.

Here we made also progress with exotic smoothness at the beginning of the year.
http://arxiv.org/abs/1201.3787
An exotic S^3xR can be partly described by a cobordism between the 3-sphere and a homology 3-sphere (Poincare sphere for instance) and vice versa. Except for the Poincare sphere, all other homology 3-spheres are negatively curved (I mean at least one component of the curvature tensor is negatively curved), a corrolary of Perelmans work.
Therefore we get the change:
postive curvature -> negative curvature -> positive curvature
For this case we explicitely solve the Friedman equations including the dust matter (p=0) and obtain inflation (I mean an exponential increase) which stops.

Also one word about the interesting claims of Carlip.
It is an amazing fact from general manifold theory that the simple 2-disk is one of the important tools. (I recommend a proceeding article of Michael Freedman "Working and playing wit the 2-disk") Therefore the dominance of 2-dimensional objects around the Planck scale was not amazing for me (I remember Loll et.al. got also this result in CDT).

 

[marcus]

Wonderful video talk by Wolfgang Wieland!
http://pirsa.org/12020129/
Goes back to the original complex Ashtekar variables and goes forward to the new double spinor version of Loop developed by Dupuis, Freidel, Livine, Speziale, Tambornino...

Maïte Dupuis is currently a visitor at Perimeter, there seems to be a convergence of people interested in this "twistorial" or dual spinor version of Loop.

I've been watching Wieland's lecture and was quite impressed. See what you think.

Torsten, you are pointing out suggestive parallels with the differential topology approach you have in progress. It would certainly be remarkable if there proved to be a solid bridge.

At first it seemed very strange to be going back to the original complex version of the Ashtekar variables. But he makes it look like a convincing move, and somehow the immirzi parameter reappears as a real number, which I would never have expected!

 

[marcus]

It's clear that there are some shifts going on. Generational, geographical, and even (on a minor level) formal.

Loop is fast moving. It isn't easy to keep in one's sights. The "target" that one is trying to describe and follow is evolving rapidly.

Generationally, we have to watch more carefully some younger representatives of the mainstream Loop.
Wolfgang Wieland, Eugenio Bianchi, Maite Dupuis, Simone Speziale, Etera Livine... (not a complete list.)
Also we should notice first-time faculty positions, some in comparatively new places, for people who were only recently postdocs:
Engle made faculty at Florida Atlantic
Sahlmann, Giesel and Meusberger made faculty at Erlangen
Singh faculty at LSU
Dittrich faculty at Perimeter

Bianchi, Haggard, Agullo are giving talks at the April APS in Atlanta. These are comparatively young researchers. Two of the talks are invited. These are not the only Loop talks at the APS meeting--I just mention these three because of the generational angle.
There seems to be some increased activity at UC Berkeley. Bianchi was just here and gave two talks.

In the formalism department, you could say that the "paradigm" of Loop is shifting towards what Dupuis, Speziale, Tambornino describe in their January 2012 paper
Spinors and Twistors in Loop gravity and Spin Foams

For me, the paper which best characterizes the new Loop wave is Wieland's
Twistorial phase space for complex Ashtekar variables
together with his PIRSA talk of 29 February. I have now viewed the whole 80 minutes, including the questons and discussion and I think it is a "must watch".

Geographically, there seems to be a shift from Europe to North America. Part of this is that Perimeter is so strong. It grabs many of the creative young people and if it does not get them on a longer term basis then it brings them there for one month visits to collaborate with people there already. For instance: Maite Dupuis, Marc Geiller and Wolfgang Wieland are all three currently visiting. There is some kind of critical mass effect. The next biannual Loops conference, Loops 2013, will be at Perimeter. Plus another factor is that the Usa has some catching up to do in Loop, which means faculty openings and growth at the newer centers south of the border.

Here's an informal window to help follow geographical movement:
http://sites.google.com/site/grqcrumourmill/
Sample postdoc moves in 2012:
Ed Wilson-Ewing/ Marseille -> LSU
Marc Geiller/ Paris -> Penn State
Thomas Cailleteau/ Grenoble -> Penn State
Philipp Höhn/ Utrecht -> Perimeter
Faculty:
Hanno Sahlmann/ Pohang -> Erlangen
Renate Loll/ Utrecht -> Nijmegen
Note that three of the postdoc moves are in the general direction Europe-->Usa

 

[marcus]

Earlier I was trying to find a write up that would preview the content of Agullo's invited talk at the April meeting of the American Physical Society. The best source, I now realize, is this set of ILQGS slides by William Nelson:
http://relativity.phys.lsu.edu/ilqgs/nelson101811.pdf
and the corresponding audio
http://relativity.phys.lsu.edu/ilqgs/nelson101811.wav
or
http://relativity.phys.lsu.edu/ilqgs/nelson101811.aif

Ah hah! I found a March 2011 ILQGS talk by Agullo
http://relativity.phys.lsu.edu/ilqgs/agullo032911.pdf
Observational signatures in LQC

He refers to work in progress by Ashtekar, William Nelson, and himself. This is precisely what is apparently not yet written up so I can't find on arxiv. It would be the basis of his invited presentation at the American Physical Society April meeting in Atlanta:

http://meetings.aps.org/Meeting/APR12/Event/170160
Beyond the standard inflationary paradigm
Ivan Agullo (Penn State)
... In this talk we introduce a completion of the inflationary paradigm from a (loop) quantum gravity point of view, by addressing gravitational issues that have been open both for the background geometry and perturbations. These include a quantum gravity treatment of the Planck regime from which inflation arises... In addition, this approach provides examples of effects that may have observational implications, that may provide a window to test the basic quantum gravity principles...

Google "ILQGS" and get http://relativity.phys.lsu.edu/ilqgs/
...Scroll down to March 2011 to get links to audio and slides of Agullo's talk.
...

And scroll down to October 2011 for Nelson's

William Nelson's talk is a "must-hear". It's some very good work (as Lee Smolin comments at the end) and is going to change how we view cosmology. It is joint work by Agullo, Ashteker, Nelson, and it just happens that Nelson gave the ILQGS presentation and Agullo will present it at the April APS in Atlanta.

ILQGS also has an interesting blog where various presentations are discussed by OTHER researchers, who often give more basic intuitive explanations of what the talk is about. Brizuela (AEI) comments on Nelson's talk, Julian Barbour (!) comments on Tim Koslowski's talk about shape dynamics, Frank Hellmann (AEI) on Jacek Puchta's about an extenstion of Spinfoam...
Check out the blog, pedagogically it complements the seminar talks and makes them more accessible.
http://ilqgs.blogspot.com/
Some future talks listed here:
http://relativity.phys.lsu.edu/ilqgs/schedulesp12.html
Note Diaz-Polo upcoming talk on Loop BH evaporation (there's a relevance to obs. testing):
http://arxiv.org/abs/1109.4239

 

[marcus]

Something I've heard a lot in talks recently is "the Loop hypothesis".

It gives a useful perspective for understanding what the various QG formulations called Loop have in common.
It is the hypothesis that you can TRUNCATE the dynamic geometry of GR to finite degrees of freedom and then recover the continuous for all practical purposes.

The Loop truncation is to consider making geometric measurements at only a FINITE SET OF POINTS. So you naturally get a graph of places where you measured some volumes and some face areas between adjacent chunk volumes. The details of what constitute possible geometric measurements are not important---angles and lengths are also allowed.

What matters is the observer can only make a finite number of measurements, and that defines the state.

I'm thinking that's what science is about:

The aim of quantitative science is to explain what we can observe and to predict thereabout .

And we never get to make more than a finite number of observations.

So a state of nature (nature's geometry) is naturally going to be truncated to a finite set of points with adjacency relations and whatever labels.
The Loop hypothesis is that this is sufficient to explain and predict what we can observe. It's minimalist. The hypothesis (a kind of gamble) is that this will prove to be sufficient to recover the continuous classical picture by taking more and more points (more elaborate networks of observation).

 

[atyy]

I think there are two different truncations.

In Rovelli's Zakopane, he talks about a truncation which is a good approximation.

The FGZ idea is that the full space can be split into nice parts and the continuum recovered exactly (not just for all practical purposes) by joining them together. The idea is that is one can do that, one just needs to quantize each part separately.

 

[marcus]

...
The FGZ idea is that the full space can be split into nice parts and the continuum recovered exactly (not just for all practical purposes) by joining them together. The idea is that is one can do that, one just needs to quantize each part separately.

Perhaps I don't understand, or I see FGZ doing something different from you. Piecewise flat decomposition with all the curvature concentrated at the joints---approximating the full range of continuously curving geometries, but not reproducing the full range exactly.

For me, what FGZ does is one further step in the process that goes back to the 1990s of finding the most mathematically convenient way to implement the Loop hypothesis*---truncating geometry to a finite number of degrees of freedom, truncating to N degrees of freedom and then letting N→∞.

There are several, many, ways this has been tried. It is all the same quest. You may wish to focus on just two initiatives: Zakopane and FGZ. But I do not wish to restrict my view that way.

Remember the Lewand--Asht measure, the holonomy-flux algebra, the Lewand--Okol--Sahl--Thiemann theorem? I see it as all part of the same journey.

I suppose that history could replace the Zako formulation and keep some features of it.

I particularly like the Hilbertspace of squareintegrable functions defined on a cartesian product of G where the Lie Group G can refer to either the rotations or the full Lorentz. And I like the gamma map from SU(2) reps to SL(2,C) reps. I hope those features are kept, but who can say?
Suppose the group G becomes somehow twistorial? It would still be like Zako, square integrable functions on G^E=#edges in a way, but it would also be different. Or suppose the hilbertspace of functions on the group manifold become not complex-valued but somethingelse valued?
I really liked Wolfgang Wieland's pirsa talk. It gave me a glimpse of where the further evolution of this "loop hypothesis" could go.

Maybe neither Zako or FQZ is final or exactly right. It would be a shock if it were
The important thing is to have something simple definite and clear--mathematically well-defined--at each step along the way. Zako served as that last year and perhaps also this year. We have to keep our eyes open for what will take shape by spring of 2013, when another Loops conference is coming due.

*I was just listening to Marc Geiller talk about the FGZ work:
http://relativity.phys.lsu.edu/ilqgs/geiller022812.pdf
http://relativity.phys.lsu.edu/ilqgs/geiller022812.wav
He calls it the "Loop assumption" instead of the Loop hypothesis, and he says concretely what he means on slide #8 early in the talk. I have the impression now that I hear many people using this idea, which has entered the shared vocabulary of the Loop community. Perhaps it was always one of the shared concepts but I didn't notice it until recently.

 

[atyy]

So are FGZ talking about what Rovelli calls the graph expansion, which he distinguishes from the vertex expansion? http://arxiv.org/abs/1102.3660 (p19).