Instability in ${\cal N}=4$ supersymmetric Yang-Mills theory on $S^3$ at finite density

TL;DR

This paper investigates the stability of ${ m N}=4$ supersymmetric Yang-Mills plasma on a three-sphere at finite density, revealing how curvature influences dynamical and thermodynamic instabilities.

Contribution

It analyzes the effects of $S^3$ curvature on the dynamical and thermodynamic stability of the plasma, highlighting differences in how curvature impacts these instabilities.

Findings

Increasing $S^3$ curvature stabilizes charge transport at low temperatures.

Thermodynamic instability persists regardless of $S^3$ volume fluctuations.

Dynamical and thermodynamic instabilities are affected differently by curvature.

Abstract

Homogeneous and isotropic equilibrium states of strongly coupled ${\cal N}=4$ supersymmetric Yang-Mills charged plasma in ${\mathbb R}^3$ with equal chemical potentials for the maximal Abelian subgroup of the $R$-symmetry group become dynamically unstable below some critical temperature. The instabilities arise in the $R$-symmetry charge transport, precisely when the equilibrium state becomes thermodynamically unstable. We study the fate these correlated instabilities when the theory is placed on $S^3$. The curvature of the three-sphere affects the onset of the dynamical and the thermodynamic instabilities differently: increasing the curvature at low temperatures can stabilize its transport, but leave the plasma thermodynamically unstable. Thermodynamic stability is never recovered provided the $S^3$ volume is allowed to fluctuate.