# Foliated Field Theory and String-Membrane-Net Condensation Picture of Fracton Order

## TL;DR

This paper introduces a new foliated field theory and a string-membrane-net condensation model to describe foliated fracton order, a novel phase of matter with layered structures affecting excitation mobility.

## Contribution

It presents the first foliated field theory and a lattice model for fracton phases, expanding the theoretical framework beyond traditional topological order.

## Key findings

- Developed a foliated field theory for fracton phases
- Constructed a lattice model with string-membrane-net condensation
- Provided insights into excitation mobility restrictions

## Abstract

Foliated fracton order is a qualitatively new kind of phase of matter. It is similar to topological order, but with the fundamental difference that a layered structure, referred to as a foliation, plays an essential role and determines the mobility restrictions of the topological excitations. In this work, we introduce a new kind of field theory to describe these phases: a foliated field theory. We also introduce a new lattice model and string-membrane-net condensation picture of these phases, which is analogous to the string-net condensation picture of topological order.