Genus two partition functions of extremal conformal field theories Academic Article uri icon

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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).

publication date

  • August 1, 2007