Anomalous transport from holography: Part II

This is a second study of chiral anomaly induced transport within a holographic model consisting of anomalous $U(1)_V\times U(1)_A$ Maxwell theory in Schwarzschild-$AdS_5$ spacetime. In the first part, chiral magnetic/separation effects (CME/CSE) are considered in presence of a static spatially-inhomogeneous external magnetic field. Gradient corrections to CME/CSE are analytically evaluated up to third order in the derivative expansion. Some of the third order gradient corrections lead to an anomaly-induced negative $B^2$-correction to the diffusion constant. We also find non-linear in $B$ modifications to the chiral magnetic wave (CMW). In the second part, we focus on the experimentally interesting case of the axial chemical potential being induced dynamically by a constant magnetic and time-dependent electric fields. Constitutive relations for the vector/axial currents are computed employing two different approximations: (a) derivative expansion (up to third order) but fully nonlinear in the external fields, and (b) weak electric field limit but resuming all orders in the derivative expansion. A non-vanishing non-linear axial current (CSE) is found in the first case. Dependence on magnetic field and frequency of linear transport coefficient functions (TCFs) is explored in the second.
Comment: v1: 25 pages, 5 multi-figures; v2: published version, 35 pages, several paragraphs added to explain resummed hydro and the technique used to resum gradients within linear approximation, two appendices added to supplement calculational details in sections 3 and 4, refs added