Fractons in curved space

TL;DR

The paper develops a covariant framework to couple simple fracton field theories to curved, Aristotelian spacetimes, focusing on models with a conserved $U(1)$ charge and dipole moment. By introducing clock forms, degenerate spatial metrics, and dipole gauge data, it derives Ward identities and the dipole algebra in curved space, and demonstrates an obstruction to covariantly coupling the symmetric tensor gauge theory, pointing to a mixed gauge–gravitational anomaly. The analysis generalises to higher multipole moments, including a conserved quadrupole moment, and provides a first-order formulation that clarifies the curved-space symmetry algebra and currents. A Higgs-phase construction can realise a gauge theory in curved space, suggesting a path to consistent transport and hydrodynamic descriptions of fracton systems. Overall, the work lays foundational tools for studying fracton transport, symmetry breaking, and anomalies in curved backgrounds.

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.