Fractons in curved space

TL;DR

This paper develops a framework for coupling fracton field theories with conserved charges to curved spacetime, revealing a mixed gauge-gravitational anomaly and generalizing to higher conserved moments like quadrupoles.

Contribution

It introduces a consistent method to couple fracton theories to curved backgrounds and uncovers a mixed gauge-gravitational anomaly in symmetric tensor gauge theories.

Findings

Established a stress-energy tensor for fracton theories in curved space

Identified a mixed gauge-gravitational anomaly in symmetric tensor gauge theory

Generalized the framework to include higher conserved moments like quadrupoles

Abstract

We consistently couple simple continuum field theories with fracton excitations to curved spacetime backgrounds. We consider homogeneous and isotropic fracton field theories, with a conserved $U(1)$ charge and dipole moment. Coupling to background fields allows us to consistently define a stress-energy tensor for these theories and obtain the respective Ward identities. Along the way, we find evidence for a mixed gauge-gravitational anomaly in the symmetric tensor gauge theory which naturally couples to conserved dipoles. Our results generalise to systems with arbitrarily higher conserved moments, in particular, a conserved quadrupole moment.