A holographic perspective on Gubser-Mitra conjecture

TL;DR

This paper demonstrates a holographic proof of the Gubser-Mitra conjecture linking thermodynamic and dynamical instabilities in gravitational backgrounds, and explores sound wave behavior in Little String Theory at high energies.

Contribution

It provides a holographic perspective on the Gubser-Mitra conjecture and identifies a tachyonic mode as a dual to sound waves in gauge theories.

Findings

Negative specific heat implies imaginary sound speed.

Tachyonic quasinormal mode corresponds to sound wave in dual gauge theory.

High-energy LST exhibits purely imaginary sound speed near Hagedorn temperature.

Abstract

We point out an elementary thermodynamics fact that whenever the specific heat of a system is negative, the speed of sound in such a media is imaginary. The latter observation presents a proof of Gubser-Mitra conjecture on the relation between dynamical and thermodynamic instabilities for gravitational backgrounds with a translationary invariant horizon, provided such geometries can be interpreted as holographic duals to finite temperature gauge theories. It further identifies a tachyonic mode of the Gubser-Mitra instability (the lowest quasinormal mode of the corresponding horizon geometry) as a holographic dual to a sound wave in a dual gauge theory. As a specific example, we study sound wave propagation in Little String Theory (LST) compactified on a two-sphere. We find that at high energies (for temperatures close to the LST Hagedorn temperature) the speed of sound is purely imaginary. This implies that the lowest quasinormal mode of the finite temperature Maldacena-Nunez background is tachyonic.