One loop partition function of six dimensional conformal gravity using heat kernel on AdS

TL;DR

This paper calculates the one-loop partition function of six-dimensional conformal gravity on AdS space using heat kernel methods, revealing contributions from Einstein gravity, ghosts, and massive modes.

Contribution

It introduces a group theoretic approach to compute heat kernels for arbitrary spin fields on AdS, applied specifically to six-dimensional conformal gravity.

Findings

Partition function includes Einstein gravity, conformal ghost, and massive modes.

Heat kernel method effectively computes contributions of symmetric transverse traceless fields.

Provides insights into quantum aspects of six-dimensional conformal gravity.

Abstract

We compute the heat kernel for the Laplacians of symmetric transverse traceless fields of arbitrary spin on the $AdS$ background in even number of dimensions using the group theoretic approach introduced in \cite{Gopakumar:2011qs} and apply it on the partition function of six dimensional conformal gravity. The obtained partition function consists of the Einstein gravity, conformal ghost and two modes that contain mass.