Fracton-Elasticity Duality

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.