Comments on Foliated Gauge Theories and Dualities in 3+1d

TL;DR

This paper develops foliated gauge field theories in 3+1 dimensions to describe fracton orders, revealing dualities and constructing models for SSPT phases with subsystem symmetries, advancing understanding of exotic topological phases.

Contribution

It introduces new foliated gauge theories in 3+1d, establishes dualities between electric and magnetic models, and constructs a foliated lattice model for SSPT phases with subsystem symmetries.

Findings

Foliated gauge theories describe fracton orders with and without matter.

A duality exists between electric and magnetic foliated models.

Constructed a lattice model for SSPT phases with subsystem symmetry.

Abstract

We investigate the properties of foliated gauge fields and construct several foliated field theories in 3+1d that describe foliated fracton orders both with and without matter, including the recent hybrid fracton models. These field theories describe Abelian or non-Abelian gauge theories coupled to foliated gauge fields, and they fall into two classes of models that we call the electric models and the magnetic models. We show that these two classes of foliated field theories enjoy a duality. We also construct a model (using foliated gauge fields and an exactly solvable lattice Hamiltonian model) for a subsystem-symmetry protected topological (SSPT) phase, which is analogous to a one-form symmetry protected topological phase, with the subsystem symmetry acting on codimension-two subregions. We construct the corresponding gauged SSPT phase as a foliated two-form gauge theory. Some instances of the gauged SSPT phase are a variant of the X-cube model with the same ground state degeneracy and the same fusion, but different particle statistics.