Anomalous Dimensions for Conserved Currents from Holographic Dilatonic Models to Superconductivity

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.