Quivers, Lattice Gauge Theories and Fractons

TL;DR

This paper explores how quiver gauge theories with $SU(N)$ groups can produce lattice gauge theories with matter that exhibit fractonic behavior, linking gauge theory structures to exotic phases.

Contribution

It introduces a framework connecting quiver gauge theories to fractonic lattice models, extending recent proposals and analyzing their symmetry and phase structure.

Findings

Identification of $ ext{Z}_N$ 1-form symmetry in these theories

Wilson loops as order parameters for phase transitions

Connection to higher-dimensional theory deconstruction

Abstract

We argue that quiver gauge theories with $SU(N)$ gauge groups give rise to lattice gauge theories with matter possessing fractonic properties, where the lattice is the quiver itself. This idea extends a recent proposal by Razamat. This class of theories exhibit a $\mathbb{Z}_N$ 1-form global symmetry that can be used to classify their phases. The order parameter of this transition is the expectation value of Wilson loops, which correspond to mesonic operators in the underlying quiver gauge theory. We discuss how this perspective naturally fits with the deconstruction of a higher dimensional theory.