Chiral non-Abelian domain walls in the Ginzburg-Landau theory

TL;DR

This paper explores chiral non-Abelian domain walls within a Ginzburg-Landau framework for dense QCD, revealing their properties through analytical and numerical methods in a simplified sigma-model limit.

Contribution

It introduces a novel analysis of chiral non-Abelian domain walls in a generalized Ginzburg-Landau model, including reduction to sine-Gordon equations and numerical validation.

Findings

Proves nonexistence of domain walls in certain vacua.

Reduces complex equations to sine-Gordon and double sine-Gordon forms.

Numerical results support the sigma-model approximation.

Abstract

In this paper, we study chiral non-Abelian domain walls in a phase of unconventional vacua of the Ginzburg-Landau model for dense QCD, by considering a wider range of parameters space not directly deduced from QCD. The phase is characterized by asymmetric vacuum-expectation values (VEVs), for example with the left scalar field, corresponding to the left quark-quark condensate, having a nonvanishing VEV and the right field having a vanishing one. The domain wall soliton interpolates between this vacuum and another where the left and right scalar fields switch roles. We study this formal possibility, but not any mechanism to generate these vacua non-perturbatively at finite density or finite temperature. Using a strong-coupling, or sigma-model limit, we are able to reduce the full dynamical complex matrix valued equations of motion to the sine-Gordon, a generalization of the sine-Gordon and a generalization of the double sine-Gordon equations. In this limit, we prove nonexistence of domain walls in one of the vacua studied here and we find full numerical computations to converge to the sigma-model limit for many cases, with some exceptions that we discuss.