Counter-examples to the correlated stability conjecture

TL;DR

This paper provides explicit counter-examples to the Correlated Stability Conjecture by demonstrating phase transitions near black brane horizons, challenging the idea that thermodynamic instability always implies dynamical instability.

Contribution

The paper presents concrete counter-examples to the CSC involving phase transitions near horizons, and discusses potential revisions to the conjecture.

Findings

Counter-examples to the CSC are demonstrated.

N=1* gauge theory exhibits a second order phase transition.

The examples involve phase transitions near black brane horizons.

Abstract

We demonstrate explicit counter-examples to the Correlated Stability Conjecture (CSC), which claims that the horizon of a black brane is unstable precisely if that horizon has a thermodynamic instability, meaning that its matrix of susceptibilities has a negative eigenvalue. These examples involve phase transitions near the horizon. Ways to restrict or revise the CSC are suggested. One of our examples shows that N=1* gauge theory has a second order chiral symmetry breaking phase transition at a temperature well above the confinement scale.