Topological M-theory as Unification of Form Theories of Gravity

TL;DR

This paper proposes a topological M-theory framework unifying various form theories of gravity across dimensions, revealing connections between topological models, quantum gravity, and string dualities.

Contribution

It introduces a topological M-theory that unifies form theories of gravity and links different models through dimensional reductions and dualities.

Findings

Classical solutions involve G_2 holonomy metrics on 7-manifolds.

Reductions yield 6D A and B topological models, 4D loop quantum gravity, and 3D Chern-Simons gravity.

Insights into the wavefunction nature of topological string partition functions and holographic links to Yang-Mills theory.

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 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.