Abstract
Nonlinear transport phenomena induced by chiral anomaly are explored within a 4D field theory defined holographically as U(1)_Vtimes U(1)_A Maxwell–Chern–Simons theory in Schwarzschild-AdS_5. In presence of weak constant background electromagnetic fields, the constitutive relations for vector and axial currents, resummed to all orders in the gradients of charge densities, are encoded in nine momenta-dependent transport coefficient functions (TCFs). These TCFs are first calculated analytically up to third order in gradient expansion, and then evaluated numerically beyond the hydrodynamic limit. Fourier transformed, the TCFs become memory functions. The memory function of the chiral magnetic effect (CME) is found to differ dramatically from the instantaneous response form of the original CME. Beyond hydrodynamic limit and when external magnetic field is larger than some critical value, the chiral magnetic wave (CMW) is discovered to possess a discrete spectrum of non-dissipative modes.
Highlights
The constitutive relations should be considered as “off-shell” relations, because they treat the charge density ρ (ρ5) as independent of J (J5)
Via inverse Fourier transform, the chiral magnetic effect (CME)/chiral separation effect (CSE) memory function is, σχ (t) dωe−iωt σχ (ω, q = 0)
At q = 0, for the remaining transport coefficient functions (TCFs) we discover some universal dependence: σaχ H vanishes; σaχ H, DH, D H do not depend on the chemical potentials at all; σ1 is linear in κ2μμ 5; σ3 is linear in κμ ; σ3 is linear in κμ 5; σ2 has a normal component independent of the chemical potentials and anomaly induced correction which is linear in κ2(μ 2 + μ 25)
Summary
The constitutive relations should be considered as “off-shell” relations, because they treat the charge density ρ (ρ5) as independent of J (J5). Transport phenomena nonlinear in external fields were realised recently [46] to be of critical importance in having a self-consistent evolution of chiral plasma This argument, together with the causality discussions mentioned earlier, would lead to the conclusion that the constitutive relations (2) should contain infinitely many “nonlinear” transport coefficients in order to guarantee applicability of the constitutive relations in a broader regime. This triggered strong interest in nonlinear chiral transport phenomena within chiral kinetic theory (CKT) [47,48,49,50]. The objective of present work is to explore all order gradient resummation for nonlinear transport effects induced by the chiral anomaly, further extending the results of Refs.
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