Anomalous Dimensions for Conserved Currents from Holographic Dilatonic Models to Superconductivity

          @misc{ scivideos_PIRSA:18060038,
            doi = {10.48660/18060038},
            url = {https://pirsa.org/18060038},
            author = {Phillips, Philip},
            keywords = {},
            language = {en},
            title = {Anomalous Dimensions for Conserved Currents from Holographic Dilatonic Models to Superconductivity },
            publisher = {Perimeter Institute for Theoretical Physics},
            year = {2018},
            month = {jun},
            note = {PIRSA:18060038 see, \url{https://scivideos.org/pirsa/18060038}}
          }
          

Abstract

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.