Renormalization group flows of the N-component Abelian Higgs model

Flows of the couplings of a theory of an N-component (complex) scalar field coupled to electrodynamics are 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 indispensable to obtain such a result. Ward-Takahashi identities are analyzed in the presence of the regulator, and their compatibility with the flow equation is investigated in detail.