Holographic Responses of Fermion Matter

TL;DR

This paper uses holography to study fermionic matter in a D4-D8 brane system, revealing Fermi liquid properties such as linear heat capacity and zero sound, with no finite-momentum singularities in current correlations.

Contribution

It demonstrates holographic evidence of Fermi liquid behavior in a strongly coupled fermionic system with baryon charge.

Findings

Heat capacity vanishes linearly with temperature.

Zero sound mode observed with speed matching hydrodynamic sound.

No singularities in current two-point functions at finite momentum.

Abstract

We consider the $D4-D8-\bar{D8}$ brane system which serves as ultraviolet completion of the Nambu-Jona-Lasinio model, where the only degrees of freedom carrying baryon charge are fermions. By turning on chemical potential for this charge one may expect the formation of the Fermi liquid ground state. At strong coupling we use the dual holographic description to investigate the responses of the system to small perturbations. In the chirally symmetric phase we find that the density dependent part of the heat capacity vanishes linearly with temperature. We also observe a zero sound excitation in the collisionless regime, whose speed is equal to that of normal sound in the hydrodynamic regime. Both the linear dependence of the heat capacity and the existence of zero sound are properties of the Fermi liquid ground state. We also compute the two-point function of the currents at vanishing frequency but do not find any singularities at finite values of the momentum.