The heat kernel on AdS₃ and its applications

Abstract

We derive the heat kernel for arbitrary tensor fields on S³and (Euclidean) AdS₃ 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 AdS₃. We apply this to the calculation of the one loop partition function of N = 1 supergravity on AdS3. 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.