Holographic Charged Fluid with Chiral Electric Separation Effect

Abstract

Hydrodynamics with both vector and axial currents is under study within a holographic model, consisting of canonical $U(1)_V\times U(1)_A$ gauge fields in an asymptotically AdS$_5$ black brane. When gravitational back-reaction is taken into account, the chiral electric separation effect (CESE), namely the generation of an axial current as the response to an external electric field, is realized naturally. Via fluid/gravity correspondence, all the first order transport coefficients in the hydrodynamic constitutive relations are evaluated analytically: they are functions of vector chemical potential $\mu$, axial chemical potential $\mu_5$ and the fluid's temperature $T$. Apart from the proportionality factor $\mu\mu_5$, the CESE conductivity is found to be dependent on the dimensionless quantities $\mu/T$ and $\mu_5/T$ nontrivially. As a complementary study, frequency-dependent transport phenomena are revealed through linear response analysis, demonstrating perfect agreement with the results obtained from fluid/gravity correspondence.