Renyi entropies and C_T for higher derivative free scalars and spinors on even spheres

TL;DR

This paper derives explicit formulas for Re9nyi entropies and central charges of higher derivative free scalars and spinors on even spheres, using spectral methods and connecting conformal anomalies with hyperbolic free energy.

Contribution

It provides a unified spectral approach to compute Re9nyi entropies and central charges for higher derivative fields on even spheres, extending previous scalar results to spinors.

Findings

Explicit formulas for Re9nyi entropies in various dimensions.

Field theoretic derivation of central charge formulas for higher derivative scalars and spinors.

Connection between conformal anomaly and hyperbolic free energy.

Abstract

General expressions for the R\'enyi entropies and central charges for higher derivative free spinors and scalars on even spheres are obtained using a direct spectral method on a compact lune division of the sphere. Formulae and numbers are rapidly obtained for any dimension and order of derivative. The relation between the conformal anomaly and the hyperbolic free energy is briefly explored using standard expansions. A field theoretic derivation of the central charge formula for higher derivative scalars in any (even) dimension, given by Osborn and Stergiou and by Gliozzi {\it et al}, is thereby provided. The corresponding extension to spinors is made. Generalised Bernoulli polynomials play an important technical role.