## 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 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 language | English (US) |
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Title of host publication | From Fields to Strings |

Subtitle of host publication | Circumnavigating Theoretical Physics: Ian Kogan Memorial Collection |

Publisher | World Scientific Publishing Co. |

Pages | 1606-1647 |

Number of pages | 42 |

Volume | 1 |

ISBN (Electronic) | 9789812775344 |

ISBN (Print) | 9789812389558 |

DOIs | |

State | Published - Jan 1 2005 |

## All Science Journal Classification (ASJC) codes

- Physics and Astronomy(all)