Abstract
We review briefly properties of chiral liquids, or liquids with massless fermionic constituents. We concentrate on three effects, namely, the low ratio of viscosity η to entropy density s, chiral magnetic and vortical effects. We sketch standard derivations of these effects in the hydrodynamic approximation and then concentrate on possibile unifying approach which is based on consideration of the (anomalously) conserved axial current. The point is that the conservation of chirality is specific for the microscopic, field-theoretic description of massless fermions and their interactions. On the macroscopic side, the standard hydrodynamic equations are not consistent, generally speaking, with conservation of a helical macroscopic motion. Imposing extra constraints on the hydrodynamics might resolve this “clash-of-symmetries” paradox.
Highlights
By chiral liquids one understands media with massless fermionic constituents interacting in a chiral invariant way
The same is to be true for the chiral vortical effect (2) since it is related to the standard chiral anomaly through the substitution (7)
Theory of chiral liquids is an exciting subject since chiral liquids possess remarkable properties
Summary
By chiral liquids one understands media with massless fermionic constituents interacting in a chiral invariant way. Dynamics of chiral liquids on microscopical level is not similar to that of superfluids In both cases one expects dissipation-free flow of currents in equilibrium. Where μ5 is the chiral chemical potential, μ5 = μR − μL, e is the electric charge of a massless Dirac fermion of the underlying fied theory, Bμ = 1/2 μνρσuνFρσ, uν is the 4-velocity of an element of the liquid and Fρσ is the external electromagnetic field strength tensor. It was found that the effect is not specific for the holographic description and can be derived within the standard hydrodynamic approach [2] There is another prediction which remains specific for holography and has good chances to be true phenomenologically. Field-theoretic approach to derivation of (3) in case of the black-hole physics was elaborated first in [7] while in Ref. [8] it was argued that the ratio (3) represents a universal lower bound consistent with the uncertainty principle
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