Chiral transport in strong fields from holography

Abstract

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,...

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