Chern-simons gauge theory and the AdS3/CFT2 correspondence

Sergei Gukov, Emil Martinec, Gregory Moore, Andrew Strominger

Research output: Chapter in Book/Report/Conference proceedingChapter

6 Scopus citations


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 AdS3 string theory is the modular-invariant partition function of the dual CFT on the boundary. This is a puzzle because AdS3 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 AdS3 string theory, where the role of the spectator boson is played by other degrees of freedom in the theory.

Original languageEnglish (US)
Title of host publicationFrom Fields to Strings
Subtitle of host publicationCircumnavigating Theoretical Physics: Ian Kogan Memorial Collection
PublisherWorld Scientific Publishing Co.
Number of pages42
ISBN (Electronic)9789812775344
ISBN (Print)9789812389558
StatePublished - Jan 1 2005

All Science Journal Classification (ASJC) codes

  • Physics and Astronomy(all)


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