A Black Hole Farey Tail
Robbert Dijkgraaf, Juan Maldacena, Gregory Moore, and Erik Verlinde

TL;DR
This paper derives an exact formula for elliptic genus Fourier coefficients of Calabi-Yau manifolds, facilitating analysis of AdS/CFT correspondence and phase transitions in D1/D5 systems.
Contribution
It provides a novel exact expression for elliptic genus Fourier coefficients, enabling new insights into AdS3/CFT2 and D1/D5 phase diagrams.
Findings
Exact Fourier coefficient expression for elliptic genera.
Insights into SL(2,Z) invariant phase diagrams.
Analysis of deconfining transitions in D1/D5 systems.
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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Taxonomy
TopicsBlack Holes and Theoretical Physics · Algebraic Geometry and Number Theory · Geometry and complex manifolds
