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arXiv · 0707.3437

Genus Two Partition Functions of Extremal Conformal Field Theories

Davide Gaiotto·Xi Yin
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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).

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Davide Gaiotto, Xi Yin. 2007-07-23. Genus Two Partition Functions of Extremal Conformal Field Theories. https://doi.org/10.1088/1126-6708%2F2007%2F08%2F029

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