## Advances in Theoretical and Mathematical Physics

- Adv. Theor. Math. Phys.
- Volume 9, Number 4 (2005), 603-665.

### Topological M-theory as unification of form theories of gravity

Robbert Dijkgraaf, Sergei Gukov, Andrew Neitzke, and Cumrun Vafa

#### 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 self-dual sector of loop quantum gravity in four 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 four dimensions and A model topological strings on twistor space.

#### Article information

**Source**

Adv. Theor. Math. Phys., Volume 9, Number 4 (2005), 603-665.

**Dates**

First available in Project Euclid: 3 April 2006

**Permanent link to this document**

https://projecteuclid.org/euclid.atmp/1144070454

**Mathematical Reviews number (MathSciNet)**

MR2201108

**Zentralblatt MATH identifier**

1129.81066

#### Citation

Dijkgraaf, Robbert; Gukov, Sergei; Neitzke, Andrew; Vafa, Cumrun. Topological M-theory as unification of form theories of gravity. Adv. Theor. Math. Phys. 9 (2005), no. 4, 603--665. https://projecteuclid.org/euclid.atmp/1144070454