Anomaly matching, (axial) Schwinger models, and high-T super Yang-Mills domain walls

TL;DR

The paper examines how discrete 't Hooft anomalies constrain the nonperturbative dynamics of the charge-$q$ Schwinger model and uses this to illuminate domain-wall physics in high-temperature 4D gauge theories. By solving the model exactly, it identifies a mixed anomaly between the discrete chiral symmetry $Z_{2q}^{d\chi}$ and the center symmetry $Z_q^{C}$, realized as a central extension in the symmetry algebra, with $q$ degenerate vacua. It then shows that the axial version of the $q=2$ Schwinger model arises on the worldvolume of high-$T$ domain walls between center-broken vacua in $SU(2)$ $\mathcal{N}=1$ SYM, inheriting the bulk anomaly via inflow and saturating it with wall degrees of freedom. The wall dynamics features a nonzero fermion condensate and a perimeter law for spacelike Wilson loops, paralleling aspects of the low-temperature bulk theory, and the work outlines generalizations to multiple adjoint fermions and lattice tests to probe these predictions.

Abstract

We study the discrete chiral- and center-symmetry 't Hooft anomaly matching in the charge-$q$ two-dimensional Schwinger model. We show that the algebra of the discrete symmetry operators involves a central extension, implying the existence of $q$ vacua, and that the chiral and center symmetries are spontaneously broken. We then argue that an axial version of the $q$$=$$2$ model appears in the worldvolume theory on domain walls between center-symmetry breaking vacua in the high-temperature $SU(2)$ ${\cal N}$$=$$1$ super-Yang-Mills theory and that it inherits the discrete 't Hooft anomalies of the four-dimensional bulk. The Schwinger model results suggest that the high-temperature domain wall exhibits a surprisingly rich structure: it supports a non-vanishing fermion condensate and perimeter law for spacelike Wilson loops, thus mirroring many properties of the strongly coupled four-dimensional low-temperature theory. We also discuss generalizations to theories with multiple adjoint fermions and possible lattice tests.