# Functional renormalization group approach to color superconducting phase transition

## TL;DR

This paper uses the functional renormalization group to analyze the nature of the color superconducting phase transition, finding it to be inherently first-order due to gluon fluctuations in three dimensions.

## Contribution

It demonstrates that gluon fluctuations prevent an infrared fixed point, establishing the first-order nature of the transition in color superconductivity.

## Key findings

- Gluon fluctuations eliminate the infrared fixed point in 3D.
- Color superconductivity exhibits a first-order phase transition.
- Analysis based on the beta function in scalar SU(N_c) gauge theories.

## Abstract

We investigate the order of the color superconducting phase transition using the functional renormalization group approach. We analyze the Ginzburg-Landau effective theory of color superconductivity and more generic scalar $SU(N_c)$ gauge theories by calculating the $\beta$ function of the gauge coupling in arbitrary dimension $d$ based on two different regularization schemes. We find that in $d=3$, due to gluon fluctuation effects, the $\beta$ function never admits an infrared fixed point solution. This indicates that, unlike the ordinary superconducting transition, color superconductivity can only show a first-order phase transition.