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

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.