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

TL;DR

This paper investigates anomaly matching in 2D Schwinger models and links it to high-temperature super Yang-Mills domain walls, revealing rich symmetry-breaking phenomena and potential lattice testability.

Contribution

It demonstrates the connection between 2D anomaly structures and 4D super-Yang-Mills domain walls, highlighting new insights into symmetry breaking and anomaly inheritance.

Findings

Discrete symmetry operators form a central extension.

Existence of q vacua due to symmetry algebra.

Domain walls exhibit fermion condensates and Wilson loop behavior.

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.