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. Our construction comprises a description of all types of two-dimensional defects, 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 the defects to the dual gauge fields, and from gauge invariance we derive continuity equations for the defect currents and the expected mobility restrictions of elasticity defects.