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arXiv · hep-th/0403225

Chern-Simons Gauge Theory and the AdS(3)/CFT(2) Correspondence

Sergei Gukov·Emil Martinec·Gregory Moore·Andrew Strominger
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Abstract

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.

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Sergei Gukov, Emil Martinec, Gregory Moore, Andrew Strominger. 2004-03-22. Chern-Simons Gauge Theory and the AdS(3)/CFT(2) Correspondence. https://doi.org/10.1142/9789812775344_0036

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