Fermi surface behavior in the ABJM M2-brane theory

Abstract

We calculate fermionic Green's functions for states of the three-dimensional ABJM M2-brane theory at large N using the gauge-gravity correspondence. We embed extremal black brane solutions in four-dimensional maximally supersymmetric gauged supergravity, obtain the linearized Dirac equations for each spin-1/2 mode that cannot mix with a gravitino, and solve these equations with infalling boundary conditions to calculate retarded Green's functions. For generic values of the chemical potentials, we find Fermi surfaces with universally non-Fermi liquid behavior, matching the situation for four-dimensional N=4 Super-Yang-Mills. Fermi surface singularities appear and disappear discontinuously at the point with all chemical potentials equal, reminiscent of a quantum critical point. One limit of parameter space has zero entropy at zero temperature, and fermionic fluctuations are perfectly stable inside an energy region around the Fermi surface. An ambiguity in the quantization of the fermions is resolved by supersymmetry.