Space-dependent symmetries and fractons

TL;DR

Space-dependent symmetries and fractons develop a symmetry-based program to understand fracton phases via polynomial shift symmetries and their realization as symmetric tensor gauge theories. The work connects these ideas to elasticity through elastic dualities, showing how Cauchy, quasicrystal, and Cosserat media map to fracton gauge structures and defect charges. It also outlines effective field theories and hydrodynamics for fractons, including fracton condensates and subdiffusive transport under multipole conservation. The review highlights geometric and diffeomorphism considerations, inverse Higgs constraints, and key open questions about gauge structures, curved backgrounds, and experimental realizations, charting a path for future progress in this rapidly evolving field.

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.