Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2004-11-05
Adv.Theor.Math.Phys.9:603-665,2005
Physics
High Energy Physics
High Energy Physics - Theory
65 pages, 2 figures, harvmac; v2: references added, small corrections/clarifications
Scientific paper
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.
Dijkgraaf Robbert
Gukov Sergei
Neitzke Andrew
Vafa Cumrun
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