Gradient resummation for nonlinear chiral transport: an insight from holography

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Anomaly-induced transport phenomena in presence of strong external electromagnetic fields are explored within a 4D field theory defined holographically as U (1) V × U (1) A Maxwell-Chern-Simons theory in Schwarzschild-AdS 5 . Two complementary studies are reported. In the first one, we present results on the Ohmic conductivity, diffusion constant, chiral magnetic conductivity, and additional anomaly-induced transport coefficients as functions of external e/m fields. Next, gradient resummation in a constant background magnetic field is performed. All-order resummed constitutive relations are parameterised by four momenta-dependent transport coefficient functions (TCFs). A highlight of this part is a thorough study of non-dissipative chiral magnetic waves (CMW) in strong magnetic fields.ArXiv ePrint: 1903.00896 where ρ, ρ 5 are vector and axial charge densities, and T is temperature. The dynamics of the plasma is governed by the "conservation laws" (continuity equations)(1.2)Note that as a result of the chiral anomaly, the global U (1) A current is no longer conserved. κ is the chiral anomaly coefficient (κ = eN c /(24π 2 ) for SU (N c ) gauge theory with a massless Dirac fermion in the fundamental representation and e is the electric charge). The constitutive relations (1.1) should be derived from the underlying microscopic theory. Yet, it is almost never feasible, even approximately. A great deal of modelling is inevitably employed in practice, frequently based on (truncated) gradient expansion and/or weak field approximations. Both approximations, and especially the latter one, can be inadequate. This can happen in an experimental setup, say, in chiral materials such as Weyl semimetals, in which e/m fields E and B can be controlled externally. Alternatively, plasma instabilities could generate strong fields dynamically and thus drive the system outside the applicability range of the constitutive relations. In all such cases the constitutive relations must be revised. The necessity to properly define chiral MHD in presence of strong external e/m fields motivates our study.In the hydrodynamic limit, the gradient expansion at each order is fixed by thermodynamics and symmetries, up to a finite number of transport coefficients (TCs). Diffusion constant, DC conductivity and shear viscosity are the most familiar examples of the lowest order TCs. However, "naive" truncation of the gradient expansion explicitly breaks relativistic invariance and thus leads to serious conceptual problems such as causality violation. Beyond conceptual issues, truncation of the gradient expansion results in numerical instabilities rendering the entire framework unreliable. Causality is restored when all order gradient terms are included, in a way providing a UV completion to the "old" hydrodynamic effective theory. The resummation generalises the concept of TC to transport coefficient functions (TCFs), which are functionals of ∂ t and ∇ 2 (or equivalently functions of frequency ω and three-momentum squared q 2 in Fourier space). Therefore,...

Section: Summary Of the Results: Part IIsupporting

confidence: 60%

Section: Summary Of the Results: Part IImentioning

confidence: 99%

Section: Part I: Gradient Expansion In External E/m Fieldsmentioning

confidence: 99%

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confidence: 99%

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Chiral transport in strong fields from holography

Demircik

Lublinsky

2019

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“…The anisotropic hydrodynamic regime of Einstein-Maxwell theory (including a Chern-Simons term) with a strong external magnetic field will be explored in [68]. In that reference, Kubo formulae are derived relating 2point correlation functions to a multitude of transport coefficients, mentioned in part already in [69][70][71][72], see also [73][74][75][76]. It is important to note that [68] considers external non-dynamical electromagnetic fields and is hence different from modern magnetohydrodynamics with dynamical electromagnetic fields, as discussed e.g.…”

Section: Resultsmentioning

confidence: 99%

Correlations far from equilibrium in charged strongly coupled fluids subjected to a strong magnetic field

Cartwright

Kaminski

2019

Within a holographic model, we calculate the time evolution of 2-point and 1point correlation functions (of selected operators) within a charged strongly coupled system of many particles. That system is thermalizing from an anisotropic initial charged state far from equilibrium towards equilibrium while subjected to a constant external magnetic field. One main result is that thermalization times for 2-point functions are significantly (approximately three times) larger than those of 1-point functions. Magnetic field and charge amplify this difference, generally increasing thermalization times. However, there is also a competition of scales between charge density, magnetic field, and initial anisotropy, which leads to an array of qualitative changes on the 2-and 1-point functions. There appears to be a strong effect of the medium on 2-point functions at early times, but approximately none at later times. At strong magnetic fields, an apparently universal thermalization time emerges, at which all 2-point functions appear to thermalize regardless of any other scale in the system. Hence, this time scale is referred to as saturation time scale. As extremality is approached in the purely charged case, 2-and 1-point functions appear to equilibrate at infinitely late time. We also compute 2-point functions of charged operators. Our results can be taken to model thermalization in heavy ion collisions, or thermalization in selected condensed matter systems.

Nonlinear chiral transport from holography

Demircik

Lublinsky

2019

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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-AdS 5 . 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 nonlinear 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.