Entanglement entropy and $C_T$ for monodromy defects of fields on odd-dimensional spheres

TL;DR

This paper studies how spherical monodromy defects affect entanglement entropy and the central charge of free conformal scalar fields on odd-dimensional spheres, revealing negative central charges for certain fluxes and providing explicit formulas for special cases.

Contribution

It provides numerical analysis and closed-form results for the impact of monodromy defects on entanglement entropy and central charge in odd-dimensional spheres, including the explicit $d o\infty$ limit.

Findings

Central charge becomes negative for certain flux parameters.

Closed-form expressions obtained for $Z_2$ monodromy case.

Explicit $d o\infty$ limit of $C_T$ is $-6/\pi$.

Abstract

The effect of a spherical monodromy defect on the entanglement entropy and central charge $C_T$ of a free conformal scalar field propagating on an odd-dimensional sphere is investigated. As on even spheres the central charge becomes negative for a range of the flux parameter, $\delta$, with possible implications for reflection positivity. The work is mostly numerical but closed forms are found for the $Z_2$ monodromy ($\delta=1/2$) yielding an explicit $d\to\infty$ limit, $C_T\to -6/\pi$