Partition functions and entanglement entropy: Weyl graviton and conformal higher spin fields

TL;DR

This paper analyzes the partition functions and entanglement entropy of conformal higher spin fields and Weyl gravitons in four dimensions, revealing their relations on different geometries and implications for non-unitarity.

Contribution

It establishes the relation of partition functions on Weyl equivalent spaces and explores their implications for entanglement entropy and non-unitarity in conformal higher spin theories.

Findings

Partition functions relate on different geometries with edge contributions.

Logarithmic coefficients are halved on $AdS_4$ compared to $S^4$.

Spectrum of quasinormal modes shows additional states indicating non-unitarity.

Abstract

We establish the relation of partition functions of conformal higher spin fields on Weyl equivalent spaces in $d=4$ dimension. We express the partition function of Weyl graviton and conformal higher spin fields as an integral over characters on $S^1\times AdS_3$, $S^4$, and $AdS_4$. We observe that the partition function of conformal higher spins on hyperbolic cylinders differs from the partition function on $S^4$ by the `edge' contribution. The logarithmic coefficient obtained from the character integral of the partition function of conformal higher spins on $AdS_4$ is the half of that obtained from the partition function on $S^4$. We evaluate the entanglement entropy and the conformal dimension of the twist operator from the partition function on the hyperbolic cylinder. The conformal dimension of the co-dimension two twist operator enables us to find a linear relation between Hofman-Maldacena variables which we use to show the non-unitarity of the theory. We observe that the spectrum of the quasinormal modes of conformal higher spins obtained from the bulk character contains additional distinct states compared to the spectrum of unitary massless higher spin fields.