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.
Highlights
We will consider the partition function of the conformal gravity in six dimensions for the combination of the conformal invariants such that their form coincides with the holographic anomaly of multiple coincident M5-branes [6, 9]
There, the one loop partition function consists of the one-loop partition function coming from Einstein gravity, conformal ghost and partially massless mode, and one massive mode [25]
In the computation of the partition function for six dimensional conformal gravity we obtain the expression in terms of one loop determinants that belong to symmetric transverse traceless fields
Summary
The “ghost” term that defines the determinants that we obtain when we eliminate the gauge degrees of freedom to which we conventionally refer to as ghost determinants, Dhμν, which denotes the path integral over the perturbations hμν around the background thermal Euclidean AdS6, and exp(−δ(2)S), the exponential of the second variation of the action (2.17). The first determinant denotes partially massless mode while the second one belongs to the massive mode It has been studied in a paper that investigates the quantum conformal higher spin (CHS) models where one obtains the partition function written in terms of determinants, that agrees with (2.34) in the six dimensions for spin two case [25]. We evaluate the above partition function of conformal gravity in six dimensions computing the heat kernel using the group theoretic approach
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