  The effect of a co--dimension--2 spherical monodromy defect on the
free--field theory of a conformal scalar is investigated. The conformal anomaly
is computed (in two ways) and thence the R\'enyi and entanglement entropies.
The $C_T$ central charge is found to be negative for a range of monodromy
flux.The calculations are pursued for any even dimensional sphere. A Possible
conflict with existing results is raised.
