Topological Unification of M-theory and LQG?

[selfAdjoint]

I don't know if this paper was commented on here while I was away at Christmas time, but I was just pointed to it by a paper on today's arxiv and I think it desrves notice.

http://arxiv.org/abs/hep-th/0411073

Robert Dijkgraaf, Sergei Gukov, Andrew Neitzke, and Cumrun Vafa; Toplogical M-theory as unification of Form Theories of Gravity.

So far I have only read the abstract:

We introduce a notion of topological M-theory and argue that it provides a unification of form theories of gravity in various dimensions. Its classical solutions involve G_2 holonomy metrics on 7-manifolds, obtained from a topological action for a 3-form gauge field introduced by Hitchin. We show that by reductions of this 7-dimensional theory one can classically obtain 6-dimensional topological A and B models, the topological sector of loop quantum gravity in 4 dimensions, and Chern-Simons gravity in 3 dimensions. We also find that the 7-dimensional M-theory perspective sheds some light on the fact that the topological string partition function is a wavefunction, as well as on S-duality between the A and B models. The degrees of freedom of the A and B models appear as conjugate variables in the 7-dimensional theory. Finally, from the topological M-theory perspective we find hints of an intriguing holographic link between non-supersymmetric Yang-Mills in 4 dimensions and A model topological strings on twistor space.

An ambitious claim, for sure, and the paper I was reading today, assumes it is a successful one.

 

[marcus]

glad you called this to the attention of the rest of us!
what was the paper on today's arxiv that referred to it?

(BTW it does not matter whether or not we spotted this
0411 paper back last year because I, at least, would not have had enough
background to get anything from it, but now things have changed
and even if people did see it earlier it is high time for a second look)

Here is the audio of a talk by Vafa
http://www.fields.utoronto.ca/audio/04-05/topstrings/vafa/

given at January 2005 Topological String conference in Toronto.
the talk could be listened to with this paper in hand, I guess.

 

[marcus]

Ah! I think the paper you are reading from today's arxiv must be
http://arxiv.org/abs/gr-qc/0502004

A Background Independent Description of Physical Processes
Authors: M. Spaans
Comments: 5 pages

A mathematical structure is presented that allows one to define a physical process independent of any background. That is, it is possible, for a set of objects, to choose an object from that set through a choice process that is defined solely in terms of the objects in the set itself. It is conjectured that this background free structure is a necessary ingredient for a self-consistent description of physical processes and that these same physical processes are determined by the absence of any background. The properties of the mathematical structure, Q, are equivalent to the three-dimensional topological manifold 2T^3 + 3S^1xS^2 (two three-tori plus three handles) embedded in four dimensions. The topology of Q provides the equations of motion for, and the properties of, fields on Q in closed form, and reproduces QED and Einstein gravity.

 

[marcus]

selfAdjoint, I still cannot get anything out of the 0411 Dijkgraaf et al paper.
I looked at it when it came out, and just now had a hopeful second look, but no go.

that is all right because maybe other people here at PF can and will deal with the paper-----Alejandro could, I guess.

there is reference [34] at the top of page 11 which is to Smolin
"Invitation to LQG", right by equation (3.12)
so there is a modest connection to LQG here, it seems to me,
but nothing for anybody to write home about, or so I guess.

I continue somewhat excited by the perturbative approach initiated by Freidel and Starodubtsev (perhaps that crowds out other things I should be looking at)

 

[selfAdjoint]

Ah! I think the paper you are reading from today's arxiv must be
http://arxiv.org/abs/gr-qc/0502004

A Background Independent Description of Physical Processes
Authors: M. Spaans
Comments: 5 pages

Yes, that's it. I just didn't get aroung to putting in the link.

 

[MTd2]

This article still seems interesting, but has not got many citations about the main topic of this thread. Do you think such unification is possible after these years? Marcus?

 

[MTd2]

These 2 were the only article that cited the topic article in the context of LQG.

1)It was uploaded 1 month after the last post of 2005. And this article from Smolin has got no after on this topic

http://arxiv.org/abs/hep-th/0503140v1

A quantization of topological M theory

Lee Smolin
(Submitted on 17 Mar 2005)
A conjecture is made as to how to quantize topological M theory. We study a Hamiltonian decomposition of Hitchin's 7-dimensional action and propose a formulation for it in terms of 13 first class constraints. The theory has 2 degrees of freedom per point, and hence is diffeomorphism invariant, but not strictly speaking topological. The result is argued to be equivalent to Hitchin's formulation. The theory is quantized using loop quantum gravity methods. An orthonormal basis for the diffeomorphism invariant states is given by diffeomorphism classes of networks of two dimensional surfaces in the six dimensional manifold. The hamiltonian constraint is polynomial and can be regulated by methods similar to those used in LQG.
To connect topological M theory to full M theory, a reduction from 11 dimensional supergravity to Hitchin's 7 dimensional theory is proposed. One important conclusion is that the complex and symplectic structures represent non-commuting degrees of freedom. This may have implications for attempts to construct phenomenologies on Calabi-Yau compactifications.

2)This is one from Herman Nicolai, 1 month before the beginning of this thread, but almost 3 years before the new "fixed" vertex.

http://arxiv.org/abs/hep-th/0501114

Loop quantum gravity: an outside view

Hermann Nicolai, Kasper Peeters, Marija Zamaklar
(Submitted on 14 Jan 2005 (v1), last revised 18 Sep 2005 (this version, v4))
We review aspects of loop quantum gravity in a pedagogical manner, with the aim of enabling a precise but critical assessment of its achievements so far. We emphasise that the off-shell (`strong') closure of the constraint algebra is a crucial test of quantum space-time covariance, and thereby of the consistency, of the theory. Special attention is paid to the appearance of a large number of ambiguities, in particular in the formulation of the Hamiltonian constraint. Developing suitable approximation methods to establish a connection with classical gravity on the one hand, and with the physics of elementary particles on the other, remains a major challenge.