Leo Radzihovsky (University of Colorado, Boulder)
I will discuss a recent discovery that elasticity theory of a two-dimensional crystal is dual to a fracton tensor gauge theory, providing a concrete realization of the fracton phenomenon. The disclinations and dislocations respectively map onto charges and dipoles of the tensor gauge theory. The fractionalized mobility of fractons matches the constrained dynamics of lattice defects. This duality leads to predictions for fractonic phases and phase transitions, such as the counterparts to the commensurate crystal, supersolid, hexatic, and isotropic fluid phases of the elasticity theory. Extensions of this duality to generalized elasticity theories provide a route to discovery of new fracton models.