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The bulk partition function of pure Chern-Simons theory on a three-manifoldis a state in the space of conformal blocks of the dual boundary RCFT, andtherefore transforms non-trivially under the boundary modular group. Incontrast the bulk partition function of AdS(3) string theory is themodular-invariant partition function of the dual CFT on the boundary. This is apuzzle because AdS(3) string theory formally reduces to pure Chern-Simonstheory at long distances. We study this puzzle in the context of massiveChern-Simons theory. We show that the puzzle is resolved in this context by theappearance of a chiral "spectator boson" in the boundary CFT which restoresmodular invariance. It couples to the conformal metric but not to the gaugefield on the boundary. Consequently, we find a generalization of the standardChern-Simons/RCFT correspondence involving "nonholomorphic conformal blocks"and nonrational boundary CFTs. These generalizations appear in thelong-distance limit of AdS(3) string theory, where the role of the spectatorboson is played by other degrees of freedom in the theory.Comment: 43 pages, harvma

CHERN–SIMONS GAUGE THEORY AND THE AdS3/CFT2 CORRESPONDENCE

CHERN–SIMONS GAUGE THEORY AND THE AdS₃/CFT₂ CORRESPONDENCE