  Flows of the couplings of a theory of an N-component (complex) scalar field
coupled to electrodynamics is investigated using the functional renormalization
group formalism in d dimensions in covariant gauges. We find charged fixed
points for any number of components in d=3, in accordance with the findings of
[G. Fejos and T. Hatsuda, Phys. Rev. D 93, 121701 (2016)] for N=1. It is argued
that the appropriate choice of the regulator matrix is indispensible to obtain
such a result. Ward-Takahashi identites are analyzed in the presence of the
regulator, and their compatibility with the flow equation is investigated in
detail.
