On Stability and Transport of Cold Holographic Matter

TL;DR

This paper investigates the stability of zero-temperature, finite density states in a holographic model of supersymmetric Yang-Mills theory, finding no instabilities and analyzing meson spectra using gauge-gravity duality.

Contribution

It provides a detailed analysis of meson spectra and stability in a holographic setup at zero temperature and finite density, employing novel numerical techniques.

Findings

No evidence of instabilities in the meson spectrum

Discovery of a pole on the imaginary frequency axis in a scalar meson correlator

Confirmation of stability despite finite entropy density at zero temperature

Abstract

We use gauge-gravity duality to study the stability of zero-temperature, finite baryon density states of N=4 supersymmetric SU(Nc) Yang-Mills theory coupled to a single massive fundamental-representation N=2 hypermultiplet in the large-Nc and large-coupling limits. In particular, we study the spectrum of mesons. The dual description is a probe D7-brane in anti-de Sitter space with a particular configuration of worldvolume fields. The meson spectrum is dual to the spectrum of fluctuations of worldvolume fields about that configuration. We use a combination of analytical and numerical techniques to compute the spectrum, including a special numerical technique designed to deal with singular points in the fluctuations' equations of motion. Despite circumstantial evidence that the system might be unstable, such as a finite entropy density at zero temperature and the existence of instabilities in similar theories, we find no evidence of any instabilities, at least for the ranges of frequency and momenta that we consider. We discover a pole on the imaginary frequency axis in a scalar meson two-point function, similar to the diffusive mode in the two-point function of a conserved charge.