Genus Two Partition Functions of Extremal Conformal Field Theories
High Energy Physics - Theory
2009-11-18 v1
Abstract
Recently Witten conjectured the existence of a family of "extremal" conformal field theories (ECFTs) of central charge c=24k, which are supposed to be dual to three-dimensional pure quantum gravity in AdS3. Assuming their existence, we determine explicitly the genus two partition functions of k=2 and k=3 ECFTs, using modular invariance and the behavior of the partition function in degenerating limits of the Riemann surface. The result passes highly nontrivial tests and in particular provides a piece of evidence for the existence of the k=3 ECFT. We also argue that the genus two partition function of ECFTs with k<11 are uniquely fixed (if they exist).
Keywords
Cite
@article{arxiv.0707.3437,
title = {Genus Two Partition Functions of Extremal Conformal Field Theories},
author = {Davide Gaiotto and Xi Yin},
journal= {arXiv preprint arXiv:0707.3437},
year = {2009}
}
Comments
14 pages