Fermi surface behavior in the ABJM M2-brane theory

TL;DR

This paper uses gauge-gravity duality to analyze fermionic Green's functions in the ABJM M2-brane theory, revealing non-Fermi liquid behavior, Fermi surface discontinuities at quantum critical points, and stable fermionic excitations under certain conditions.

Contribution

It provides the first detailed holographic calculation of fermionic Green's functions in the ABJM M2-brane theory, identifying non-Fermi liquid behavior and quantum critical phenomena.

Findings

Fermi surfaces exhibit non-Fermi liquid behavior for generic chemical potentials.

Discontinuous appearance and disappearance of Fermi surface singularities at symmetric chemical potentials.

Existence of a parameter regime with zero entropy at zero temperature and stable fermionic fluctuations.

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.