Partition functions and elliptic genera from supergravity

TL;DR

This paper develops a systematic approach to compute partition functions in string/M-theory on AdS(3) x M, including corrections, to better understand the AdS(3)/CFT(2) correspondence and the Farey tail expansion.

Contribution

It introduces a detailed spacetime framework for partition function calculations, incorporating subleading corrections and extending to N=2 theories with higher derivative effects.

Findings

Enhanced understanding of the Farey tail expansion from bulk physics

Systematic inclusion of subleading corrections in partition functions

Extension to N=2 theories with higher derivative effects

Abstract

We develop the spacetime aspects of the computation of partition functions for string/M-theory on AdS(3) xM. Subleading corrections to the semi-classical result are included systematically, laying the groundwork for comparison with CFT partition functions via the AdS(3)/CFT(2) correspondence. This leads to a better understanding of the "Farey tail" expansion of Dijkgraaf et. al. from the point of view of bulk physics. Besides clarifying various issues, we also extend the analysis to the N=2 setting with higher derivative effects included.