Emergent Dipole Gauge Fields and Fractons

Abstract

We present a realization of fracton-elasticity duality purely formulated in terms of ordinary gauge fields, encompassing standard elasticity and incommensurate crystals as those describing twisted bilayer graphene, quasicrystals or more general moiré lattices. Our construction comprises a description of all types of two-dimensional defects: disclinations, dislocations, discompressions and point-like defects, and takes into account body forces and impurities. The original form of the duality in terms of tensor gauge fields is recovered after partial gauge fixing. We identify the coupling of each type of defect to the dual gauge fields, and from gauge invariance we derive generalized continuity equations for the defect currents and the expected mobility restrictions of elasticity defects.

9 pages (v3: improved expressions for the currents, comments added on sigle-valuedness of the fields)

References in corpus (14)

• Fate of spin polarization in a relativistic fluid: An entropy-current analysis
• Fractons, dipole symmetries and curved spacetime
• Hydrodynamics of spin currents
• Relativistic spin hydrodynamics with torsion and linear response theory for spin relaxation
• Non-dissipative second-order transport, spin, and pseudo-gauge transformations in hydrodynamics
• Effective Lagrangian and Topological Interactions in Supersolids
• Hydrodynamics of ideal fracton fluids
• Torsional string Newton-Cartan geometry for non-relativistic strings
• Infinite families of fracton fluids with momentum conservation
• Quantum smectic gauge theory
• Effective field theories for gapless phases with fractons via a coset construction
• Dual gauge theory formulation of planar quasicrystal elasticity and fractons
• Fracton-elasticity duality in twisted moiré superlattices
• Tearing Fractons

Cited by in corpus (2)

• Hydrodynamics of dipole-conserving fluids
• A symmetry principle for gauge theories with fractons