Talks

It is well known that the dimension of conserved currents is determined simply from dimensional analysis. However, a recent proposal is that what is strange about the conserved currents in the strange metal in the cuprate superconductors is that they carry anomalous dimensions. The basic model invoked to exhibit such behaviour is a holographic dilatonic one in which the field strength couples to the radial coordinate. I will show that the anomalous dimension in such cases arises from a fractional electromagnetism that can be thought of as a general loop-hole in Noether's second theorem. The general mechanism operative is a mass term in the IR that couples to the UV current. Such a mass that couples to the radial component of the gauge field introduces a breaking of U(1) everywhere except at the boundary. I will also show that even the Pippard kernel invoked to explain the Meissner effect in traditional low-temperature superconductors is a special case of the non-local action found here, implying that symmetry breaking is the general mechanism for fractional electromagnetisms. I will also construct the Virasoro algebra for such fractional currents and discuss the general implications for the bulk-boundary construction in holography.

I will discuss recent discovery that elasticity theory of a two-dimensional crystal is dual to a fracton tensor gauge theory, providing a concrete manifestation of the fracton phenomenon in an ordinary solid. The topological defects of elasticity theory map onto charges of the tensor gauge theory, with disclinations and dislocations corresponding to fractons and dipoles, respectively. The transverse and longitudinal phonons of crystals map onto the two gapless gauge modes of the gauge theory. The restricted dynamics of fractons matches with constraints on the mobility of lattice defects. The duality leads to numerous predictions for phases and phase transitions of the fracton system, such as the existence of gauge theory counterparts to the (commensurate) crystal, supersolid, hexatic, and isotropic fluid phases of elasticity theory. Extensions of this duality to generalized elasticity theories provide a route to the discovery of new fracton models.