Fractons, symmetric gauge fields and geometry

TL;DR

This work develops a geometric framework for gapless fracton phases with charge and dipole conservation by embedding physical spacetime into a higher-dimensional Heisenberg-like space and treating the Nambu–Goldstone mode $\phi(x)$ as an embedding coordinate. A Born–Infeld–type action for spontaneous symmetry breaking and a fully diffeomorphism- and gauge-invariant higher-rank gauge theory are constructed, with symmetric gauge fields $A_{ab}$ gauging the fracton symmetry and reducing to the known flat-space fracton electrodynamics in the appropriate limit. The formalism introduces Stueckelberg fields to preserve gauge invariance on curved backgrounds, linking fracton dynamics to gravitational structures and offering a path to covariant Ward identities and hydrodynamics for multipole-conserving systems. The approach promises further insights into fracton-elasticity dualities, connections to volume-preserving diffeomorphisms in quantum Hall contexts, and possible Chern–Simons generalizations, broadening the applicability of fracton theories to curved spacetimes.

Abstract

Gapless fracton phases are characterized by the conservation of certain charges and their higher moments. These charges generically couple to higher rank gauge fields. In this paper we study systems conserving charge and dipole moment, and construct the corresponding gauge fields propagating in arbitrary curved backgrounds. The relation between the symmetries of these class of systems and spacetime transformations is discussed. In fact, we argue that higher rank symmetric gauge theories are closer to gravitational fields than to a standard gauge theory.