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Chern-Simons Gauge Theory and the AdS_3/CFT_2 Correspondence

Gukov, Sergei and Martinec, Emil and Moore, Gregory and Strominger, Andrew (2004) Chern-Simons Gauge Theory and the AdS_3/CFT_2 Correspondence. . (Submitted)

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The bulk partition function of pure Chern-Simons theory on a three-manifold is a state in the space of conformal blocks of the dual boundary RCFT, and therefore transforms non-trivially under the boundary modular group. In contrast the bulk partition function of AdS_3 string theory is the modular-invariant partition function of the dual CFT on the boundary. This is a puzzle because AdS_3 string theory formally reduces to pure Chern-Simons theory at long distances. We study this puzzle in the context of massive Chern-Simons theory. We show that the puzzle is resolved in this context by the appearance of a chiral “spectator boson” in the boundary CFT which restores modular invariance. It couples to the conformal metric but not to the gauge field on the boundary. Consequently, we find a generalization of the standard Chern-Simons/RCFT correspondence involving “nonholomorphic conformal blocks” and nonrational boundary CFTs. These generalizations appear in the long-distance limit of AdS_3 string theory, where the role of the spectator boson is played by other degrees of freedom in the theory.

Item Type:Report or Paper (Discussion Paper)
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URLURL TypeDescription Paper
Gukov, Sergei0000-0002-9486-1762
Additional Information:(Submitted on 22 Mar 2004). March 19, 2004. We would like to thank J. Maldacena and E. Witten for discussions and C. Schweigert and N. Read for correspondence. G.M. would like to that the KITP for hospitality during the course of some of this work. This work was conducted during the period S.G. served as a Clay Mathematics Institute Long-Term Prize Fellow. The work of E.M. is supported in part by DOE grant DE-FG02-90ER40560, that of G.M. by DOE grant DE-FG02-96ER40949 and that of A.S. by DE-FG02-91ER40654.
Funding AgencyGrant Number
Department of Energy (DOE)DE-FG02-90ER40560
Department of Energy (DOE)DE-FG02-96ER40949
Department of Energy (DOE)DE-FG02-91ER40654
Record Number:CaltechAUTHORS:20160506-145809044
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:66716
Deposited By: Ruth Sustaita
Deposited On:06 May 2016 23:21
Last Modified:09 Mar 2020 13:18

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