CHERN-SIMONS Gauge Theory and the AdS3/CFT2 Correspondence
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.
- Publication:
-
From Fields to Strings: Circumnavigating Theoretical Physics: Ian Kogan Memorial Collection (in 3 Vols). Edited by SHIFMAN MISHA ET AL. Published by World Scientific Publishing Co. Pte. Ltd
- Pub Date:
- 2005
- DOI:
- 10.1142/9789812775344_0036
- arXiv:
- arXiv:hep-th/0403225
- Bibcode:
- 2005ffsc.book.1606G
- Keywords:
-
- High Energy Physics - Theory;
- Condensed Matter - Mesoscale and Nanoscale Physics
- E-Print:
- 43 pages, harvmac