# Renormalization group flows of the N-component Abelian Higgs model

## TL;DR

This paper studies the renormalization group flows of an N-component Abelian Higgs model using the functional renormalization group approach, identifying charged fixed points in three dimensions and analyzing gauge invariance issues.

## Contribution

It extends the analysis of fixed points in the Abelian Higgs model to arbitrary N and emphasizes the importance of regulator choice and Ward-Takahashi identities.

## Key findings

- Charged fixed points exist for any N in three dimensions.
- Proper regulator matrix selection is crucial for obtaining fixed points.
- Ward-Takahashi identities are compatible with the flow equations under certain conditions.

## Abstract

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.