The Fracton Gauge Principle

TL;DR

This paper develops a gauge principle-based framework to derive tensor gauge theories for fractons, particles with restricted mobility due to higher moment conservation laws, revealing their intrinsic interactions and potential for non-abelian generalizations.

Contribution

It introduces a method to obtain fracton tensor gauge theories from ungauged models by applying the gauge principle to higher moment conservation laws.

Findings

Formulated a field theory for ungauged fractons with global charge and dipole conservation.

Demonstrated how to promote these global symmetries to local gauge invariances, leading to tensor gauge fields.

Extended the approach to other subdimensional particles, paving the way for non-abelian fracton theories.

Abstract

A powerful mechanism for constructing gauge theories is to start from a theory with a global symmetry, then apply the "gauge principle," which demands that this symmetry hold locally. For example, the global phase rotation of a system of conserved charges can be promoted to a local phase rotation by coupling to an ordinary U(1) vector gauge field. More recently, a class of particles has been studied featuring not only charge conservation, but also conservation of higher moments, such as dipole moment, which leads to severe restrictions on the mobility of charges. These particles, called fractons, are known to be intimately connected to symmetric tensor gauge fields. In this work, we show how to derive such tensor gauge theories by applying the gauge principle to a theory of ungauged fractons. We begin by formulating a field theory for ungauged fractons exhibiting global conservation of charge and dipole moment. We show that such fracton field theories have a characteristic non-Gaussian form, reflecting the fact that fractons intrinsically interact with each other even in the absence of a mediating gauge field. We then promote the global higher moment conservation laws to local ones, which requires the introduction of a symmetric tensor gauge field. Finally, we extend these arguments to other types of subdimensional particles besides fractons. This work offers a possible route to the formulation of non-abelian fracton theories.