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

TL;DR

This paper uses SU(2) chiral perturbation theory to analyze the temperature dependence of topological observables and domain wall tension in QCD, including isospin-breaking effects, providing insights relevant for axion physics.

Contribution

It extends previous work by incorporating isospin-breaking effects into the analysis of topological charge cumulants and domain wall tension at finite temperature.

Findings

Topological susceptibility matches lattice data at low T but deviates at higher T.

Normalized fourth-order cumulant and domain wall tension decrease with T.

Normalized sixth-order cumulant increases with T.

Abstract

Within the framework of SU(2) chiral perturbation theory, we derive the general solution of the QCD $\theta$-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 $\theta$-vacuum domain walls, thereby offering new theoretical input on the $\theta$-vacuum properties, which are relevant for axion-related effective theories in hot QCD matter.