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Topological observables and domain wall tension from finite temperature chiral perturbation theory

Zhen-Yan Lu1,*, Quan Tang1,†, Shu-Peng Wang1,‡, Yang Huang1,§, Zhen Zhang2,∥, and Bonan Zhang3,¶

  • *Contact author: luzhenyan@hnust.edu.cn
  • †Contact author: tangquan@mail.hnust.edu.cn
  • ‡Contact author: wsp@mail.hnust.edu.cn
  • §Contact author: yanghuang@mail.bnu.edu.cn
  • ∥Contact author: zhangzhen@ihep.ac.cn
  • Contact author: bnzhang@imnu.edu.cn
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Phys. Rev. D 113, 054042 – Published 25 March, 2026

DOI: https://doi.org/10.1103/knjl-w486

Abstract

Within the framework of SU(2) chiral perturbation theory, we derive the general solution of the QCD θ vacuum for an arbitrary vacuum phase, explicitly incorporating isospin-breaking effects from the light quark mass difference, and compute the temperature dependence of the topological susceptibility, higher-order cumulants, and the domain wall tension up to next-to-leading order. We find that the topological susceptibility agrees with lattice data at low temperatures but deviates at higher temperatures as expected from the breakdown of the chiral expansion; moreover, we demonstrate that the normalized fourth-order cumulant and the domain wall tension decrease monotonically with increasing temperature, while the normalized sixth-order cumulant exhibits the opposite behavior. These results extend earlier analyses by showing how isospin breaking reshapes the full hierarchy of topological charge cumulants and the dynamics of θ-vacuum domain walls, thereby offering new theoretical input on the θ-vacuum properties, which are relevant for axion-related effective theories in hot QCD matter.

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Phys. Rev. D 113, 054042– Published 25 March, 2026
  • Received 1 November 2025
  • Accepted 4 March 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.

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