Partition Functions for Higher-Spin theories in AdS

TL;DR

This paper computes one-loop partition functions for higher-spin fields in AdS spaces, revealing connections to symmetry algebras and special functions, advancing understanding of higher-spin theories in holography.

Contribution

It provides explicit calculations of partition functions for higher-spin theories in AdS, including Vasiliev theory in AdS_5, and uncovers links to algebraic structures and combinatorial functions.

Findings

Partition functions expressed in a form suggestive of vacuum characters.

Connection established between Vasiliev theory partition function and d-dimensional MacMahon function.

Results indicate potential symmetry enhancements in higher-spin theories.

Abstract

We calculate the one-loop partition function for a massless arbitrary-spin field on quotients of a general dimensional AdS background using the results of arXiv:1103.3627. We use these results to compute the one-loop partition function for a Vasiliev theory in AdS_5. An interesting form of the answer, suggestive of a vacuum character of an enhanced symmetry algebra is obtained. We also observe a close connection between the partition function for this Vasiliev theory and the d-dimensional MacMahon function.