Abstract
This is a second study of chiral anomaly-induced transport within a holographic model consisting of anomalous U(1)_Vtimes U(1)_A Maxwell theory in Schwarzschild–AdS_5 spacetime. In the first part, chiral magnetic/separation effects (CME/CSE) are considered in the 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 modifications to the chiral magnetic wave nonlinear in B. 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 nonlinear axial current (CSE) is found in the first case. The dependence on magnetic field and frequency of linear transport coefficient functions is explored in the second.
Highlights
Introduction and summaryFluid dynamics [1,2] is an effective long-wavelength description of most classical or quantum many-body systems at nonzero temperature
It is defined in terms of constitutive relations, which relate thermal expectation values of conserved currents to thermodynamical variables and external fields
The derivative expansion is fixed by thermodynamic considerations and symmetries, up to a finite number of transport coefficients, such as the viscosity, diffusion constant and conductivity
Summary
Fluid dynamics [1,2] is an effective long-wavelength description of most classical or quantum many-body systems at nonzero temperature. CME emerges from a nonzero axial chemical potential μ5 , which is usually assumed to have some background profile It is, possible to induce ρ5 (and μ5 ) dynamically through the interplay between the electric and magnetic fields, as is clear from the continuity equation (2). As for the linearised setup (10), [73,74,75,76] imposed the continuity equation and replaced the axial charge density ρ5 in favour of the external electric and magnetic fields, so the vector current there is on shell. This is in contrast to our off-shell formalism.
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