Electromagnetic instability of vacuum with instantons in the holographic plasma

Using the gauge-gravity duality, we study the electromagnetic instability of vacuum with instantons in holographic plasma. The model we employ is the D(-1)-D3 brane system in which the D(-1)-branes correspond to the instantons in holography. To take into account the flavored quarks, the coincident probe D7-branes as flavors are embedded into the bulk geometry so that the effective electromagnetic Lagrangian with flavors corresponds to the action of the D7-branes according to gauge-gravity duality. We numerically evaluate the vacuum decay rate, the critical electric field and the V-A curve of the vacuum by using the D7-brane action with various values of the electromagnetic field. It implies the particles in the plasma acquire an effective mass in the presence of instantons as it is expected in the quantum field theory, and the plasma trends to become insulating when the electric field is small. This work reveals the relation between electromagnetic and instantonic properties of the vacuum in the plasma.