The Heat Kernel on AdS_3 and its Applications

TL;DR

This paper derives the heat kernel for tensor fields on AdS_3 and its quotients, enabling explicit calculations of one-loop determinants and partition functions in supergravity, confirming theoretical predictions about their structure.

Contribution

It provides a group theoretic derivation of the heat kernel on AdS_3 and applies it to compute one-loop partition functions in supergravity.

Findings

Explicit heat kernel expressions for tensor fields on AdS_3.

Factorization of the supergravity partition function into super Virasoro characters.

Confirmation of the theoretical structure of one-loop determinants in AdS_3 supergravity.

Abstract

We derive the heat kernel for arbitrary tensor fields on S^3 and (Euclidean) AdS_3 using a group theoretic approach. We use these results to also obtain the heat kernel on certain quotients of these spaces. In particular, we give a simple, explicit expression for the one loop determinant for a field of arbitrary spin s in thermal AdS_3. We apply this to the calculation of the one loop partition function of N=1 supergravity on AdS_3. We find that the answer factorizes into left- and right-moving super Virasoro characters built on the SL(2, C) invariant vacuum, as argued by Maloney and Witten on general grounds.