Topological M-theory as Unification of Form Theories of Gravity

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.

arXiv comment65 pages, 2 figures, harvmac; v2: references added, small corrections/clarifications

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• An invitation to loop quantum gravity
• Attractors and the Holomorphic Anomaly
• Geometric Transitions, Flops and Non-Kahler Manifolds: II
• Non-supersymmetric Black Holes and Topological Strings
• Generalised geometries, constrained critical points and Ramond-Ramond fields
• Topological Symmetry of forms, N=1 Supersymmetry and S-duality on Special Manifolds
• The Topological G2 String
• A Deformation of Twistor Space and a Chiral Mass Term in N=4 Super Yang-Mills Theory
• The Ricci Curvature of Half-flat Manifolds
• A quantization of topological M theory
• Topological B-model and $\hat{c}=1$ String Theory
• Topological M Theory from Pure Spinor Formalism
• Aspects of Twistor Geometry and Supersymmetric Field Theories within Superstring Theory
• Note on a duality of topological branes
• The Chevalley group G_{2}(2) of order 12096 and the octonionic root system of E_{7}
• Taming open/closed string duality with a Losev trick
• S-duality and a large N phase transition in N=4 SYM on K3 at strong coupling
• Topological strings live on attractive manifolds
• Abelian Varieties, RCFTs, Attractors, and Hitchin Functional in Two Dimensions
• Some comments on the local curve (B-side)
• On topological M-theory