Holographic Schwinger effect and electric instability with anisotropy

Abstract

According to the gauge-gravity duality, we systematically study the Schwinger effect and electric instability with anisotropy in a top-down approach. The anisotropic black brane and bubble (soliton) background in IIB supergravity are employed and the dual theory in these backgrounds is expected to be anisotropic theory at finite temperature and anisotropic theory with confinement respectively. Then performing the potential analysis, we find due to the anisotropy, the potential barrier behaves oppositely with parallel and perpendicular electric fields, and this behavior agrees with the previous study about the quark potential with anisotropy in this system. Afterwards, we evaluate the pair production rate by solving the equation of motion for a fundamental string numerically which reveals the consistent behavior with the potential analysis. Furthermore, the probe D7-brane as flavor is introduced into the bulk in order to investigate the electric instability. The vacuum decay rate can be obtained by evaluating the imaginary part of the D7-brane action which again agrees with our potential analysis. Solving the associated constraint of gauge field strength on the flavor brane, we finally obtain the V-A curve which displays that the behavior of the conductivity is distinct in parallel and perpendicular direction which is in agreement with phenomenologically holographic approaches in anisotropic fluid. Accordingly, this work may be remarkable to study the electric features in strongly coupled anisotropic system.