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Chern-Simons theory and S-duality

Dimofte, Tudor and Gukov, Sergei (2013) Chern-Simons theory and S-duality. Journal of High Energy Physics, 2013 (5). Art. No. 109. ISSN 1126-6708. doi:10.1007/JHEP05(2013)109.

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We study S-dualities in analytically continued SL(2) Chern-Simons theory on a 3-manifold M. By realizing Chern-Simons theory via a compactification of a 6d five-brane theory on M, various objects and symmetries in Chern-Simons theory become related to objects and operations in dual 2d, 3d, and 4d theories. For example, the space of flat SL(2, C ) connections on M is identified with the space of supersymmetric vacua in a dual 3d gauge theory. The hidden symmetry h → -4π^2/h of SL(2) Chern-Simons theory can be identified as the S-duality transformation of N=4 super-Yang-Mills theory (obtained by compactifying the five-brane theory on a torus); whereas the mapping class group action in Chern-Simons theory on a three-manifold M with boundary C is realized as S-duality in 4d N=2 super-Yang-Mills theory associated with the Riemann surface C. We illustrate these symmetries by considering simple examples of 3-manifolds that include knot complements and punctured torus bundles, on the one hand, and mapping cylinders associated with mapping class group transformations, on the other. A generalization of mapping class group actions further allows us to study the transformations between several distinguished coordinate systems on the phase space of Chern-Simons theory, the SL(2) Hitchin moduli space.

Item Type:Article
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URLURL TypeDescription DOIArticle Paper
Gukov, Sergei0000-0002-9486-1762
Additional Information:© 2013 SISSA. Published for SISSA by Springer. Received: March 16, 2013. Accepted: April 20, 2013. Published: May 21, 2013. We wish thank G. Mikhalkin, G. Moore, A. Neitzke, R. van der Veen, D. Zagier, and especially D. Gaiotto and J. Teschner for many enlightening and helpful discussions. We would also like to thank the Aspen Center for Physics for their hospitality during the 2010 Summer Program, where some of the ideas presented here originated. The work of TD is supported in part by NSF Grant PHY-0969448. The work of SG is supported in part by DOE Grant DE-FG03-92-ER40701 and in part by NSF Grant PHY-0757647. Opinions and conclusions expressed here are those of the authors and do not necessarily reflect the views of funding agencies.
Group:Caltech Theory
Funding AgencyGrant Number
Department of Energy (DOE)DE-FG03-92-ER40701
Subject Keywords:Duality in Gauge Field Theories, Chern-Simons Theories, Topological Field Theories, Supersymmetric gauge theory
Issue or Number:5
Record Number:CaltechAUTHORS:20130913-112827417
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:41323
Deposited By: Ruth Sustaita
Deposited On:13 Sep 2013 20:13
Last Modified:10 Nov 2021 04:28

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