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

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 $(E,B,T,μ_5)$ space with constraint equation $σ_B B =- σE$, where $σ$ and $σ_B$ are called electric and chiral magnetic conductivity, respectively. We analyze the decay rate of a gapless system when this constraint is slightly violated.