Equilibrium Instability of Chiral Mesons in External Electromagnetic Field via AdS/CFT

TL;DR

This paper investigates the equilibrium instability of chiral mesons in a plasma under external electromagnetic fields using AdS/CFT, revealing phase transitions and growth of instability with magnetic field strength.

Contribution

It introduces a holographic model analyzing how magnetic and electric fields induce instability and phase transitions in chiral mesons, including effects of axial chemical potential.

Findings

Magnetic field and axial chemical potential induce instability even without electric field.

A phase transition between stable and unstable states is observed in gapped systems.

Instability growth is linear with magnetic field at zero temperature and large magnetic field.

Abstract

We study the equilibrium instability of chiral quarkonia in a plasma in the presence of constant magnetic and electric field and at finite axial chemical potential using AdS/CFT duality. The model in use is a supersymmetric QCD at large 't$\,$Hooft coupling and number of colors. We show that the presence of the magnetic field and the axial chemical potential even in the absence of the electric field make the system unstable. In a gapped system, a stable/unstable equilibrium state phase transition is observed and the initial transition amplitude of the equilibrium state to the non-equilibrium state is investigated. We demonstrate that at zero temperature and large magnetic field the instability grows linearly by increasing the quarkonium binding energy. In the constant electric and magnetic field, the system is in a equilibrium state if the Ohm's law and the chiral magnetic effect cancel their effects. This happens in a sub-space of $(E,B,T,\mu_5)$ space with constraint equation $\sigma_B B =- \sigma E$, where $\sigma$ and $\sigma_B$ are called electric and chiral magnetic conductivity, respectively. We analyze the decay rate of a gapless system when this constraint is slightly violated.