# High-temperature domain walls of QCD with imaginary chemical potentials

## TL;DR

This paper investigates high-temperature domain walls in QCD with imaginary chemical potentials, revealing their topological nature and anomaly-related properties through semiclassical analysis.

## Contribution

It demonstrates that high-temperature domain walls in QCD can be viewed as symmetry-protected topological orders with nontrivial gauge theories supported on the walls, analyzed via semiclassical methods.

## Key findings

- Domain walls support nontrivial massless gauge theories due to anomaly inflow.
- Semiclassical analysis matches 't Hooft anomalies for high-temperature domain walls.
- High-temperature domain walls relate to Roberge-Weiss phase transitions.

## Abstract

We study QCD with massless quarks on $\mathbb{R}^3\times S^1$ 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 semiclassical analysis to obtain the domain-wall theory, and $2$d $U(N_\mathrm{c}-1)$ gauge theories with massless fermions match the 't~Hooft anomaly. We perform these analysis for the high-temperature domain wall of $\mathbb{Z}_{N_\mathrm{c}}$-QCD and also of Roberge-Weiss phase transitions.