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The effect of a co--dimension--2 spherical monodromy defect on thefree--field theory of a conformal scalar is investigated. The conformal anomalyis 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 monodromyflux.The calculations are pursued for any even dimensional sphere. A Possibleconflict with existing results is raised.

Renyi entropy for spherical monodromy of free scalar fields in even dimensions