Foliated Quantum Field Theory of Fracton Order

TL;DR

This paper introduces a continuum foliated quantum field theory framework for describing gapped fracton orders, utilizing layered structures and foliated gauge fields to capture constrained particle mobility and dualities.

Contribution

It presents a novel foliated quantum field theory model for fracton order, incorporating foliated gauge fields and a duality that enables exfoliation of 2+1D gauge theories.

Findings

Quantized level coefficients with duality properties

Gauge invariant operators constrained to layer intersections

Duality allows decoupling of 2+1D gauge theories from the FQFT

Abstract

We introduce a new kind of foliated quantum field theory (FQFT) of gapped fracton orders in the continuum. FQFT is defined on a manifold with a layered structure given by one or more foliations, which each decompose spacetime into a stack of layers. FQFT involves a new kind of gauge field, a foliated gauge field, which behaves similar to a collection of independent gauge fields on this stack of layers. Gauge invariant operators (and their analogous particle mobilities) are constrained to the intersection of one or more layers from different foliations. The level coefficients are quantized and exhibit a duality that spatially transforms the coefficients. This duality occurs because the FQFT is a foliated fracton order. That is, the duality can decouple 2+1D gauge theories from the FQFT through a process we dub exfoliation.