High-temperature domain walls of QCD with imaginary chemical potentials

A bstractWe study QCD with massless quarks on ℝ3 × S1 under symmetry-twisted boundary conditions with small compactification radius, i.e. at high temperatures. Under suitable boundary conditions, the theory acquires a part of the center symmetry and it is spontaneously broken at high temperatures. We show that these vacua at high temperatures can be regarded as different symmetry-protected topological orders, and the domain walls between them support nontrivial massless gauge theories as a consequence of anomaly-inflow mechanism. At sufficiently high temperatures, we can perform the semi-classical analysis to obtain the domain-wall theory, and 2d U(Nc − 1) gauge theories with massless fermions match the ’t Hooft anomaly. We perform these analysis for the high-temperature domain wall of ℤNc$$ {\mathbb{Z}}_{N_{\mathrm{c}}} $$-QCD and also of Roberge-Weiss phase transitions.