Open Access
Translator Disclaimer
August 2005 Topological M-theory as unification of form theories of gravity
Robbert Dijkgraaf, Sergei Gukov, Andrew Neitzke, Cumrun Vafa
Adv. Theor. Math. Phys. 9(4): 603-665 (August 2005).


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.


Download Citation

Robbert Dijkgraaf. Sergei Gukov. Andrew Neitzke. Cumrun Vafa. "Topological M-theory as unification of form theories of gravity." Adv. Theor. Math. Phys. 9 (4) 603 - 665, August 2005.


Published: August 2005
First available in Project Euclid: 3 April 2006

zbMATH: 1129.81066
MathSciNet: MR2201108

Rights: Copyright © 2005 International Press of Boston


Vol.9 • No. 4 • August 2005
Back to Top