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

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 ($\delta =1\mathrm{/}2$) yielding an explicit $d\to \mathrm{\infty }$ limit, $C_T\to -6\mathrm{/}\pi$