  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, $C_T\to -6/\pi$
