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

Within the framework of SU(2) chiral perturbation theory, we derive the general solution of the QCD <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mi>θ</a:mi> </a:math> 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 <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"> <c:mi>θ</c:mi> </c:math> -vacuum domain walls, thereby offering new theoretical input on the <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"> <e:mi>θ</e:mi> </e:math> -vacuum properties, which are relevant for axion-related effective theories in hot QCD matter.