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

Sven Bjarke Gudnason1,* and Muneto Nitta2,3

  • 1Institute of Contemporary Mathematics, School of Mathematics and Statistics, Henan University, Kaifeng, Henan 475004, People’s Republic of China
  • 2Department of Physics & Research and Education Center for Natural Sciences, Keio University, Hiyoshi 4-1-1, Yokohama, Kanagawa 223-8521, Japan
  • 3International Institute for Sustainability with Knotted Chiral Meta Matter (WPI-SKCM2), Hiroshima University, 1-3-2 Kagamiyama, Higashi-Hiroshima, Hiroshima 739-8511, Japan

  • *Contact author: gudnason@henu.edu.cn
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Phys. Rev. D 112, 085022 – Published 24 October, 2025

DOI: https://doi.org/10.1103/blyr-wlst

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 nonperturbatively 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.

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Phys. Rev. D 112, 085022– Published 24 October, 2025
  • Received 25 June 2025
  • Accepted 24 September 2025
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