Abstract
Nonlinear transport phenomena induced by the chiral anomaly are explored within a 4D field theory defined holographically as U(1)V × U(1)A Maxwell-Chern-Simons theory in Schwarzschild-AdS5. First, in presence of external electromagnetic fields, a general form of vector and axial currents is derived. Then, within the gradient expansion up to third order, we analytically compute all (over 50) transport coefficients. A wealth of higher order (nonlinear) transport phenomena induced by chiral anomaly are found beyond the Chiral Magnetic and Chiral Separation Effects. Some of the higher order terms are relaxation time corrections to the lowest order nonlinear effects. The charge diffusion constant and dispersion relation of the Chiral Magnetic Wave are found to receive anomaly-induced non-linear corrections due to e/m background fields. Furthermore, there emerges a new gapless mode, which we refer to as Chiral Hall Density Wave, propagating along the background Poynting vector.
Highlights
Beyond conceptual issues, causality violation results in numerical instabilities rendering the entire framework unreliable
As a result of chiral anomaly, which appears in relativistic QFTs with massless fermions, global U(1)A current coupled to external electromagnetic fields is no longer conserved
We have continued exploration of nonlinear chiral anomaly-induced transport phenomena based on a holographic model with two U(1) fields interacting via a ChernSimons term
Summary
This subsection briefly summarises the series of works [24, 25, 96, 111] including the present one, so to help the reader to navigate between various studies and results. The constitutive relations (1.2) can be formally Taylor expanded in all its arguments This includes the gradient (λ), , and α expansions. The most general constitutive relations correspond to a sum of all possible terms like (2.3).. E = B = 0; all order gradient terms that are linear in the inhomogeneous fluctuations δρ, δρ, δE, δB are resummed.. E = B = 0; all order gradient terms that are linear in the inhomogeneous fluctuations δρ, δρ, δE, δB are resummed.6 This corresponds to calculating currents up to O( 1α0). In the present work, we relax some of the approximations made in [24, 25] and derive constitutive relations for the currents, up to third order in the gradient expansion. We summarise the main results of the present work, leaving all the technical details in the main text and appendix
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