Deconfinement on axion domain walls

Abstract

We study SU(Nc) gauge theories with Dirac fermions in representations ℛ of nonzero N -ality, coupled to axions. These theories have an exact discrete chiral symmetry, which has a mixed ’t Hooft anomaly with general baryon-color-flavor backgrounds, called the “BCF anomaly” in [1]. The infrared theory also has an emergent {mathrm{mathbb{Z}}}_{N_c}^{(1)} 1-form center symmetry. We show that the BCF anomaly is matched in the infrared by axion domain walls. We argue that {mathrm{mathbb{Z}}}_{N_c}^{(1)} is spontaneously broken on axion domain walls, so that nonzero N -ality Wilson loops obey the perimeter law and probe quarks are deconfined on the walls. We give further support to our conclusion by using a calculable small-circle compactification to study the multi-scale structure of the axion domain walls and the microscopic physics of deconfinement on their worldvolume.