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Topological M-theory as Unification of Form Theories of Gravity

Dijkgraaf, Robbert and Gukov, Sergei and Neitzke, Andrew and Vafa, Cumrun (2005) Topological M-theory as Unification of Form Theories of Gravity. Advances in Theoretical and Mathematical Physics, 9 (4). pp. 603-665. ISSN 1095-0761.

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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.

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Additional Information:© 2005 International Press. First available in Project Euclid: 3 April 2006. We are grateful to M. Atiyah, J. de Boer, R. Bryant, C. LeBrun, J. Louis, H. Ooguri, M. Roček, L. Smolin, C. Taubes, E. Verlinde, and S.-T. Yau for valuable discussions. We would like to thank the 2004 Simons Workshop on Mathematics and Physics and the Aspen Workshop “Strings, Branes and Superpotentials,” which led to the development of many of the ideas in this paper. We also thank the organizers of the Strings 2004 conference in Paris for providing a stimulating environment where part of this work was done. S.G. and A.N. would like to thank Caltech Particle Theory Group, where part of this work was done, for kind hospitality. This work was conducted during the period S.G. served as a Clay Mathematics Institute Long-Term Prize Fellow. S.G. was also supported in part by RFBR grant 04-02-16880. The research of A.N. and C.V. was supported in part by NSF grants PHY-0244821 and DMS-0244464. The research of R.D. was partly supported by FOM and the NWO Spinoza premium.
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Clay Mathematics InstituteUNSPECIFIED
Russian Foundation for Basic Research04-02-16880
Stichting voor Fundamenteel Onderzoek der Materie (FOM)UNSPECIFIED
Nederlandse Organisatie voor Wetenschappelijk Onderzoek (NWO)UNSPECIFIED
Issue or Number:4
Classification Code:MR2201108
Record Number:CaltechAUTHORS:20160511-091820774
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Official 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.
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:66978
Deposited By: Ruth Sustaita
Deposited On:11 May 2016 18:34
Last Modified:03 Oct 2019 10:01

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