Robbert Dijkgraaf et al: 4D 2-Form Gravity & Topological M-Theory

[marcus]

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

Robbert Dijkgraaf, Sergei Gukov, Andrew Neitzke, Cumrun Vafa

See page 11 section 3.3 "4D 2-Form Gravity"

The authors are well-known. Dijkgraaf is in Amsterdam and the others are at Harvard.

"4D 2-form gravity" serves as a general pointer in the direction of LQG and its relatives. The connection variable on which LQG is based (the configuration set consists of connections embodying possible geometries) is technically a 2-form. LQG is a 4D connection-based model of gravity so it can be termed a "4D 2-form gravity"

there are various other N-form-type gravity models with other dimensionality, like 3D and 7D etc. They don't all use 2-forms, so let's say N-form to keep it general.

what Dijkgraaf et al try to do is to include all these various-dimensioned N-form-based models-----at least in a loose general way----within a theoretical framework they call "Topological M-Theory".

As they indicate the connections are tentative----a bit fuzzy---and leave a lot of details to work out. The contact with LQG is not with something you can get your hands on and calculate with, but instead with what they call "topological LQG"-----something with the right general look AFAICS but not copying at the level of specifics.

 

[marcus]

I was reminded of an oddly similar paper by Lee Smolin and Artem Starodubtsev that came out just a year before this Dijkgraaf et al String one.

That was
http://arxiv.org/hep-th/0311163
General Relativity with a topological phase: an action principle

"An action principle is described which unifies general relativity and topological field theory. An additional degree of freedom is introduced and depending on the value it takes the theory has solutions that reduce it to
1) general relativity in Palatini form,
2) general relativity in the Ashtekar form,
3) $$\inline{F\wedge F}$$ theory for SO(5) and
4) BF theory for SO(5).
This theory then makes it possible to describe explicitly the dynamics of phase transition between a topological phase and a gravitational phase where the theory has local degrees of freedom. We also find that a boundary between a dynamical and topological phase resembles an horizon."

that Smolin paper, like the Dijkgraaf one that just came out, was also concerned with putting 4 or 5 different approaches together in a single theoretical framework. And there are other common elements as well.

 

[selfAdjoint]

Marcus, I'm not sure about the F wedge F theory, but Palatini and Ashtekar are two different ways to describe the same thing, GR, and I believe constrained BF theory is isomorphic to GR too. So having a parameter that gives these results is good, but it isn't new physics. Or am I missing something?