Space-dependent symmetries and fractons

TL;DR

This paper reviews the emerging space-dependent symmetries in effective theories of fractons, exploring their role in describing gapless fractons through elastic duality and hydrodynamics.

Contribution

It introduces and discusses novel coordinate-dependent symmetries in effective non-Lorentzian theories of fractons, highlighting their impact on understanding fracton properties.

Findings

Identification of space-dependent symmetries in fracton theories

Effective description of gapless fractons via elastic duality

Discussion of fracton hydrodynamics

Abstract

There has been a surge of interest in effective non-Lorentzian theories of excitations with restricted mobility, known as fractons. Examples include defects in elastic materials, vortex lattices or spin liquids. In the effective theory novel coordinate-dependent symmetries emerge that shape the properties of fractons. In this review we will discuss these symmetries, cover the effective description of gapless fractons via elastic duality, and discuss their hydrodynamics.