# Charged and neutral fixed points in the O(N)+O(N)-model with Abelian gauge fields

## TL;DR

This paper investigates the fixed points in a two-field Abelian-Higgs model with gauge fields, revealing multiple charged fixed points for N>2 and their implications for phase transitions.

## Contribution

It extends the analysis of fixed points in a two-field Abelian-Higgs model using the functional renormalization group, highlighting new charged fixed points for N>2.

## Key findings

- Three charged fixed points for all N>2
- Additional fixed points for N=2
- Confirmation of fixed-point structure in neutral case

## Abstract

In the Abelian-Higgs model, or Ginzburg-Landau model of superconductivity, the existence of an infrared stable charged fixed point ensures that there is a parameter range where the superconducting phase transition is second order, as opposed to fluctuation-induced first order as one would infer from the Coleman-Weinberg mechanism. We study the charged and neutral fixed points of a two-field generalization of the Abelian-Higgs model, where two N-component fields are coupled to two gauge fields and to each other, using the functional renormalization group. Focusing mostly on three dimensions, in the neutral case, this is a model for two-component Bose-Einstein condensation, and we confirm the fixed-point structure established in earlier works using different methods. The charged model is a dual theory of two-dimensional dislocation-mediated quantum melting. We find the existence of three charged fixed points for all N>2, while there are additional fixed points for N=2.