The Heat Kernel on $AdS$

TL;DR

This paper computes the heat kernel for arbitrary spin tensor fields on thermal Euclidean AdS spaces using group theoretic methods, extending previous techniques from AdS3 to higher dimensions.

Contribution

It provides a general, explicit evaluation method for the heat kernel on thermal Euclidean AdS spaces of any dimension, broadening the applicability of previous AdS3 techniques.

Findings

Explicit heat kernel expressions for arbitrary spin tensors on Euclidean AdS_N

Method applicable to other quotients and symmetric spaces

Extension of AdS3 techniques to higher dimensions

Abstract

We explicitly evaluate the heat kernel for the Laplacian of arbitrary spin tensor fields on the thermal quotient of (Euclidean) $AdS_N$ for $N\geq 3$ using the group theoretic techniques employed for $AdS_3$ in arXiv:0911.5085. Our approach is general and can be used, in principle, for other quotients as well as other symmetric spaces.