One loop partition function for Topologically Massive Higher Spin Gravity

TL;DR

This paper computes the one loop partition function for topologically massive higher spin gravity across arbitrary spins, revealing non-holomorphic factorization and suggesting a duality with a logarithmic conformal field theory extension.

Contribution

It generalizes the spin-3 TMHSG action to arbitrary spins and derives the partition function, providing evidence for a duality with a logarithmic CFT.

Findings

Partition function expressed in a product form

Evidence against holomorphic factorization

Supports duality with logarithmic CFT

Abstract

We calculate the one loop partition function for topologically massive higher spin gravity (TMHSG) for arbitrary spin by taking the spin-3 TMHSG action constructed in arXiv:1107.0915 and subsequently generalising it for an arbitrary spin. We find that the final result can be put into a product form which cannot be holomorphically factorized giving strong evidence that the topologically massive higher spin gravity is dual to a high spin extension of logarithmic CFT rather than a chiral one.