Genus Two Partition Functions of Extremal Conformal Field Theories

Details Genus Two Partition Functions of Extremal Conformal Field Theories Genus Two Partition Functions of Extremal Conformal Field Theories

2007-07-23

arxiv.org/abs/0707.3437v1

JHEP 0708:029,2007

Physics

High Energy Physics

High Energy Physics - Theory

14 pages

Scientific paper

10.1088/1126-6708/2007/08/029

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).

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