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A Black Hole Farey Tail

Robbert Dijkgraaf·Juan Maldacena·Gregory Moore·Erik Verlinde
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Abstract

We derive an exact expression for the Fourier coefficients of elliptic genera of Calabi-Yau manifolds. When applied to k-fold symmetric products of K3 surfaces the expression is well-suited to studying the AdS/CFT correspondence on AdS3 x S3. The expression also elucidates an SL(2,Z) invariant phase diagram for the D1/D5 system involving deconfining transitions in the limit as k goes to infinity.

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Robbert Dijkgraaf, Juan Maldacena, Gregory Moore, Erik Verlinde. 2007-12-08. A Black Hole Farey Tail. https://arxiv.org/abs/hep-th/0005003

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