AdS one-loop partition functions from bulk and edge characters

TL;DR

This paper derives a novel integral formula for one-loop partition functions of higher spin fields in AdS, revealing cancellations that support holographic duality and connecting to thermal partition functions.

Contribution

It introduces a character integral representation for AdS higher spin one-loop partition functions, linking bulk and edge characters and elucidating holographic correspondences.

Findings

Demonstrates cancellations between bulk and edge characters in higher-spin theories.

Shows agreement of partition functions with HS/CFT holography predictions.

Connects character integral formulas to Rindler-AdS thermal partition functions.

Abstract

We show that the one-loop partition function of any higher spin field in $(d+1)$-dimensional Anti-de Sitter spacetime can be expressed as an integral transform of an $\text{SO}(2,d)$ bulk character and an $\text{SO}(2,d-2)$ edge character. We apply this character integral formula to various higher-spin Vasiliev gravities and find miraculous (almost) cancellations between bulk and edge characters that lead to agreement with the predictions of HS/CFT holography. We also discuss about the relation between the character integral representation and Rindler-AdS thermal partition function.