$C_T$ for monodromy defects of fields on odd dimensional spheres for higher derivative propagation

TL;DR

This paper calculates the central charge $C_T$ for scalar and Dirac fields with monodromy on odd-dimensional spheres, revealing its relation to free energy derivatives and deriving closed forms for specific monodromy values.

Contribution

It provides explicit formulas for $C_T$ in odd dimensions with monodromy, extending previous even-dimensional results and analyzing its variation with flux.

Findings

$C_T$ relates to free energy derivatives via Perlmutter factor.

Closed forms for $C_T$ at specific monodromy values are derived.

Infinite dimension limits are obtained for special cases.

Abstract

The central charge $C_T$ is computed for scalar and Dirac fields propagating according to GJMS-type kinetic operators acting on odd $d$-dimensional spheres in the presence of a spherical monodromy. The relation of $C_T$ to the derivatives of the free energy on the conically deformed sphere via the Perlmutter factor leads to a numerical quadrature. The variation of $C_T$ with the monodromy flux, $\delta$, displays sign changes, exactly as in even dimensions. Closed forms for $C_T$ are derived when $\delta$ equals 0 or 1/2 with the derivative order either even or odd and shown to agree with existing, even $d$ expressions. The infinite $d$ limits are also derived in these special cases.