Holographic Dual of the Lowest Landau Level

Abstract

We describe the lowest Landau level of a quantum electron star in AdS4. In the presence of a suitably strong magnetic field, the dynamics of fermions in the bulk is effectively reduced from four to two dimensions. These two-dimensional fermions can subsequently be treated using the techniques of bosonization and the difficult many-body problem of building a gravitating, charged quantum star is reduced to solving the sine-Gordon model coupled to a gauge field and a metric. The kinks of the sine-Gordon model provide the holographic dual of the lowest Landau levels of the strongly-coupled d=2+1 dimensional boundary field theory. The system exhibits order one oscillations in the magnetic susceptibility, now arising as a classical effect in the bulk. Moreover, as the chemical potential is varied, we find jumps in the charge density, oscillations in the fractionalised charge density and plateaux in the cohesive charge densityComment: 39 pages; 8 Figure