Loop Gravity as the Dynamics of Topological Defects

[marcus]

There is a natural way to formulate Loop quantum geometry as the dynamics of line defects in a flat vacuum. Just under 2 months ago, I attended a 90 minute seminar talk on this at the UC Berkeley physics department. Unfortunately that talk is not online, but we do have an earlier talk given last year at Perimeter Institute:

http://pirsa.org/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 - 4:00 pm

It's an exciting development. I would say there is a key step that you see right around minute 14-19 and slides #10 and #11*. I already mentioned this new formulation of Loop in an earlier thread, back in February.
https://www.physicsforums.com/showthread.php?p=3782389#post3782389
The dynamics is worked out in terms of surface defects in flat 4D spacetime or you could say spinfoam.

To me it seems significant that EB chose to talk about the dynamics of defects treatment of Loop when he was out here, because he has more than one idea that he's working on--including (I hear) a possibly deeper way to understand black hole entropy and count the geometric states of the horizon.

There is a technical problem with the PIRSA video which is slightly awkward but which one can work around: the audio was recorded at a low level. You may need some additional amplification (if your computer is like mine) in order to hear clearly.

*pages 17/48 and 20/48 of the PDF, if you happen to have downloaded it.

 

[marcus]

How the dynamics is handled is interesting. In BF terms one is imposing the simplicity constraint on B only on a 2-complex--the 2-skeleton of the triangulation. (see slide #17)
So instead of unfreezing an infinite number of d.o.f. and getting GR, one unfreezes only a finite number of d.o.f. and gets a truncation of GR.

The curvature of the connection F(ω) is therefore zero everywhere in the bulk, and only nonzero on the 2-skeleton--the defects in spacetime. This represents a history of how the line defects in space could evolve.

The presenting the dynamics begins in minute 25, but then there are questions from Freidel and Smolin (possibly others too, I forget) and some discussion. So the dynamics begins again around minute 29.

IIRC dynamics begins with slide #16. Slide #17 has a lot of content and the presentation is interrupted again with a lot of questions, which is good: points get repeated more slowly. Slides 16 and 17 are e.g. on pages 30/48 and 31/48 of the PDF, if you downloaded that (I found it helps as review/reference for the talk.)

 

[marcus]

This recorded seminar talk Loop as dynamics of line defects was actually second highest in our first quarter 2012 POLL.
https://www.physicsforums.com/showthread.php?t=591299

Also according to the report I got from the Atlanta meeting of the American Physical Society this way of understanding Loop dynamic quantum geometry (as a writhing heap of line defects in otherwise flat space) was the main topic of an invited talk. These talks run 45 minutes to an hour, so Bianchi was able to give an overview of spinfoam QG and also get into this relatively new formulation of it.

At the moment I'm picturing it as a fractured piece of glass with the fractures moving all around very rapidly scrambling and rejoining etc. Or like what I see when I turn our compost pile--you have to turn it over every month or so, with a fork or spade. A writhing heap of earthworms:-D

http://pirsa.org/11090125/
Loop Gravity as the Dynamics of Topological Defects
The only thing to note is that it's better if your computer audio feeds into your hifi amp and goes to regular speakers so you can adjust the volume. This particular PIRSA is recorded with the audio level too low, at least for my laptop with my not especially good hearing.

The history of the swarm of line defects in 3D space translates into a foam of surface defects throughout a 4D spacetime region. Everybody sees this but I just add it for completeness.

 

[marcus]

I see I mentioned this already: Bianchi gave a talk about the topo. defects formulation of Loop gravity at the UC Berkeley Physics Department in February. He got a bunch of questions from a couple of senior faculty and some grad students---it sparked a lot of discussion.
I was lucky enough to be there. It was 24 February, just two months ago. All the seats in the room were taken Steve Carlip was in from UC Davis to hear the talk.

Bianchi gave two talks when he was out here in February---the other was a general introductory overview of Loop/Spinfoam QG. It drew a large audience which included undergraduate physics majors. The one on "Loop gravity as the dynamics of topological defects" was aimed at a smaller group of faculty and grad students already familiar with QG.

EDIT: I double checked and see I made a mistake in post #3, the topological defects formulation did get some emphasis in Bianchi's Atlanta talk (as I heard from someone who was there) but this was not the main topic. The talk was an invited survey of Loop&Spinfoam so it was overview, more like the other talk he gave at Berkeley.