A Black Hole Farey Tail

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.