Anomalous Dimensions for Conserved Currents from Holographic Dilatonic Models to Superconductivity

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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.