Spin Foams & AdS/CFT: Lattice Gauge Theories

[atyy]

Apparently some lattice gauge theories can be formulated as spin foams. Conrady even says "The concept of spin foams is both new and old. It is old in the sense that it is just another name for the plaquette diagrams that appear in the strong coupling expansion of lattice gauge theories". Do these lattice gauge theories have any gravity dual in the AdS/CFT sense?

Reisenberger, http://arxiv.org/abs/gr-qc/9412035
Oeckl and Pfeiffer, http://arxiv.org/abs/hep-th/0008095
Conrady, http://arxiv.org/abs/gr-qc/0504059v2

 

[atyy]

marcus has just listed in his bibliography a paper that is in the spirit of this question https://www.physicsforums.com/showpost.php?p=3222193&postcount=1451 .

http://arxiv.org/abs/1103.6264
Spin foam models with finite groups
Benjamin Bahr, Bianca Dittrich, James P. Ryan

"As we will show in this work the 4D spin foam models, which as gravity models are based on SO(4), SO(3, 1) or SU(2), can be easily generalized to finite groups (or more generally tensor categories [35]). Although the immediate interpretation as gravity models is lost one can nevertheless ask whether translation symmetries are realized and if not how these could be implemented. This question is much easier to answer for finite groups than in the full gravity case. One can therefore see these models as a test bed for the full theory. This also applies for renormalization and coarse graining techniques which need to be developed to access the large scale limit of spin foams. With finite group models it might be in particular possible to access the many–particle (that is many simplices or building blocks in the triangulation) and small spin (corresponding to small geometrical size of the building blocks) regime. This is in contrast to the few particle and large spin (semi–classical) regime [36] which is accessible so far.

In the emergent gravity approaches [37] one attempts to construct models, which do not necessarily start from gravitational or even geometrical variables, but nevertheless show features, typical of gravity."

 

[Physics Monkey]

There is this old paper my Simeon Hellerman which is partially related: http://arxiv.org/abs/hep-th/0207226

More generally, I can't figure out why there isn't a large effort trying to make a connection between holographic duality and loopy gravity approaches. Given what we know about holography already it seems to me almost guaranteed to be a gold mine. And yet apart from a few famous papers from some years ago I'm not aware of anything major being done. It's probably what I would work on if I was a loop person.

 

[atyy]

Another loopy paper thinking about gravity without gravity: http://arxiv.org/abs/1101.6078 .

Barrett explicitly says there are spin foam models of lattice gauge theory, but there is no mention of AdS/CFT, which to my mind is a realization of the spirit of induced gravity.

Strominger has a few interesting comments about induced gravity and black hole entropy here: http://arxiv.org/abs/0906.1313 .

The only loop paper I can think of that draws an explicit connection to AdS/CFT is http://arxiv.org/abs/0905.3627 .

I wonder if Krasnov is still thinking about this http://arxiv.org/abs/hep-th/0311162 . He actually preceded the current twistor craze, and is cited by Witten (though Witten's paper took a different approach, and I'm not sure Witten's paper is directly related to current fashion, except in spirit).

And yet apart from a few famous papers from some years ago I'm not aware of anything major being done.

What are these famous papers from some years ago?

 

[marcus]

...
The only loop paper I can think of that draws an explicit connection to AdS/CFT is http://arxiv.org/abs/0905.3627 ...

This paper cites Freidel Livine Ponzano-Regge work, but I don't find explicit use of spinfoams.
http://arxiv.org/abs/0804.0632 .

I think you know the paper but point to it since I didn't not see it mentioned here. May not be close enough.

 

[atyy]

BF theory with matter:

LQG:
http://arxiv.org/abs/gr-qc/0605087
http://arxiv.org/abs/0709.4235

Strings:
http://arxiv.org/abs/0805.1012
http://arxiv.org/abs/0805.1087
http://arxiv.org/abs/0805.1202
http://arxiv.org/abs/0807.1074