A holographic perspective on Gubser-Mitra conjecture

TL;DR

This work provides a clear, holographic proof of the Gubser-Mitra conjecture for gravitational backgrounds with translationally invariant horizons by showing that negative specific heat implies an imaginary speed of sound, reflecting a dynamical instability in the dual gauge theory. Focusing on Little String Theory compactified on $S^2$ via the Maldacena-Nunez background, the authors construct a 5D effective action and analyze finite-temperature deformations, deriving a high-energy (near-Hagedorn) equation of state. The hydrodynamic analysis of the lowest quasinormal mode reveals a tachyonic mode with $v_s^2 = -\frac{2}{a_0^4} + O(a_0^{-6})$ in the large-$a_0$ regime, aligning thermodynamic and dynamical instability indicators. Collectively, the results establish a concrete holographic link between thermodynamic negativity of $c_V$ and dynamical instabilities, with implications for phase structure and transport in strongly coupled gauge theories.

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.