# Fractons from vector gauge theory

## TL;DR

This paper introduces a vector gauge theory framework to describe fracton phases, revealing their origin from an unusual Gauss law and connecting to known tensor gauge theories, with lattice models illustrating the condensation mechanisms.

## Contribution

It develops a vector gauge theory approach to fractons, linking elasticity duality to fracton order and constructing lattice models demonstrating string condensation.

## Key findings

- Fracton order arises from a novel Gauss law in vector gauge theories.
- Low-energy limit reduces to known symmetric tensor gauge theories.
- Lattice models exhibit fracton phases via string-like excitation condensation.

## Abstract

Motivated by the prediction of fractonic topological defects in a quantum crystal, we utilize a reformulated elasticity duality to derive a description of a fracton phase in terms of coupled vector U(1) gauge theories. The fracton order and restricted mobility emerge as a result of an unusual Gauss law where electric field lines of one gauge field act as sources of charge for others. At low energies this vector gauge theory reduces to the previously studied fractonic symmetric tensor gauge theory. We construct the corresponding lattice model and a number of generalizations, which realize fracton phases via a condensation of string-like excitations built out of charged particles, analogous to the p-string condensation mechanism of the gapped X-cube fracton phase.