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.

Spectral weight in Chern-Simons theory with symmetry breaking

“…This is another indication that the role of η is to determine the overall presence or absence of spectral weight. It is interesting to note that Fermi shells also appear in top-down constructions in N = 4 supersymmetric Yang-Mills [25] and ABJM theory [26]. In top-down constructions the matter content of the dual field theory is known, and it was seen explicitly that Fermi shells arise from a superposition of two Fermi surfaces (which result from two distinct fermions).…”

“1k F ” singularities and finite density ABJM theory at strong coupling

“…as well as to understand the nature of fermionic excitations near the Fermi surface (via the spectral function, proportional to Im G R ). By fully decoupling 32 of the 56 spin 1/2 modes of the maximal gauged SUGRA from all other fermions, the authors of [20,21] were able to compute such fermionic two-point functions in the ABJM phase dual to AdS-RN holographically. Two important lessons from that work are:…”

TASI Lectures on Applications of Gauge/Gravity Duality

“…Here both quantizations are possible, and they are equivalent in simple backgrounds but inequivalent in the presence of other interactions. This case is relevant for 4D N = 8 gauged supergravity, where SUSY can be used to select the regular quantization; see [23,24] and for a modern discussion [62].…”

“…Instead of a doping parameter, one may vary the ratios of chemical potentials (of which one has three for the SO(6) of N = 4, and four for the SO(8) of ABJM) to produce new geometries. Holographic Fermi surfaces indeed appear in such top-down models for many fermionic fields, and interestingly, over a wide class of such top-down geometries, every fermion studied has non-Fermi liquid behavior [67,36,62]. 14 Varying the chemical potentials can also produce geometries where ν k F → 0, which can be thought of as the divergence of a correlation length [69].…”

“…In certain special IR-singular geometries with vanishing entropy, there can be perfectly stable modes in an energy band, before the non-Fermi liquid behavior returns[68,62].…”