# Flows of multicomponent scalar models with U(1) gauge symmetry

## TL;DR

This paper explores the renormalization group flows of multicomponent scalar models with U(1) gauge symmetry, revealing conditions for consistency and analyzing fixed points using the functional renormalization group method.

## Contribution

It demonstrates that adding a U(1) factor ensures the renormalizability of these scalar theories and clarifies the relation between different regularization schemes.

## Key findings

- Scalar theories are generally non-renormalizable without U(1) factors.
- Adding U(1) factors makes theories consistent and renormalizable.
- Calculated beta functions and classified fixed points.

## Abstract

We investigate the renormalization group flows of multicomponent scalar theories with $U(1)$ gauge symmetry using the functional renormalization group method. The scalar sector is built up from traces of matrix fields that belong to simple, compact Lie algebras. We find that in general these theories are non-renormalizable even at zero gauge coupling, but if we add a $U(1)$ factor to the Lie algebra structure, then they are consistent. In accordance with our earlier findings, fluctuations introduce anomalous, regulator dependent gauge contributions, which are only consistent with the flow equation for a given set of gauge fixing parameters. We establish connections between regularization procedures in the standard covariant and the $R_\xi$ gauges arguing that one is not tied by introducing regulators at the level of the functional integral, and it is allowed to switch between schemes at different levels of the calculations. We calculate $\beta$ functions, classify fixed points, and clarify compatibility of the flow equation and the Ward-Takahashi identity between the scalar wavefunction renormalization and the charge rescaling factor.