  Quantum critical behavior in 2+1 dimensions is established via holographic
methods in a 5+1-dimensional Einstein gravity theory with gauge potential form
fields of rank 1 and 2. These fields are coupled to one another via a
tri-linear Chern-Simons term with strength k. The quantum phase transition is
physically driven by the expulsion of the electric charge from inside the black
brane horizon to the outside, where it gets carried by the gauge fields which
acquire charge thanks to the Chern-Simons interaction. At a critical value
k=k_c, zero temperature, and any finite value of the magnetic field, the IR
behavior is governed by a near-horizon Lifshitz geometry. The associated
dynamical scaling exponent depends on the magnetic field. For k<k_c, the flow
towards low temperature is governed by a Reissner-Nordstrom-like black brane
whose charge and entropy density are non-vanishing at zero temperature. For k >
k_c, the IR flow is towards the purely magnetic brane in AdS_6. Its
near-horizon geometry is AdS_4 \times R^2, so that the entropy density vanishes
quadratically with temperature, and all charge is carried by the gauge fields
outside of the horizon.

High Energy Physics - Theory