Fractons in curved space

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.

37 pages; v2: Added references, flat space stress tensor of dipole-symmetric scalar theory

References in corpus (8)

• Local stabilizer codes in three dimensions without string logical operators
• Spacetime Symmetries of the Quantum Hall Effect
• Fractons, dipole symmetries and curved spacetime
• The low-energy limit of some exotic lattice theories and UV/IR mixing
• Hydrodynamics of ideal fracton fluids
• Aspects of hot Galilean field theory
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Cited by in corpus (2)

• Fractons, dipole symmetries and curved spacetime
• Infinite families of fracton fluids with momentum conservation