Valentin I. Zakharov

The Minkowski vacuum in an accelerated frame behaves like a fluid that has not only a finite temperature due to the Unruh effect, but also a finite shear viscosity. Moreover, the ratio of this viscosity to the entropy density exactly satisfies the Kovtun-Son-Starinets bound, inspired by the string theory η / s = 1 / 4 π . The origin of this viscosity is purely kinematical and is believed to be related to entanglement introduced by the Rindler horizon. We directly calculate the viscosity, entropy density, and their ratio for massless fields with spins 1 / 2 and 1. We show that locally the ratio of viscosity to entropy density can be below the limiting value 1 / 4 π at distances of the order of the thickness of the membrane corresponding to the stretched horizon, and is described by the universal function for different spins. In particular, on the membrane surface η / s = 1 / 8 π .

An Erratum to this paper has been published: https://doi.org/10.1134/S1063779625040033

By chiral effects, one understands the manifestations of chiral gauge anomaly and of gravitational chiral anomaly in hydrodynamics. In the last two to three years, our understanding of chiral effects has considerably changed. Here, we present a mini-review of two topics: first, a shift in understanding symmetry, which underlies the chiral magnetic effect and second, the interpretation of the chiral kinematical effect uncovered recently.

By anomalous transport one understands transport driven by the chiral anomalies of quantum field theory (QFT). In our case it is mostly axial current in hydrodynamical set up. The notion of duality assumes existence of two different theories whose predictions for a certain class of observables coincide with each other. In our case the observables are matrix elements of external probes, such as energy-momentum tensor or axial current, as functions of acceleration and angular velocity of the medium. Two approaches to evaluate these observables are provided by thermodynamics and by theory of motion in external gravitational fields. The corresponding duality was introduced by the authors in the year 2019. We reiterate the basic points of the argumentation and highlight new points brought in by later development.

The usual Minkowski vacuum in an accelerated frame of reference is known to look like a “thermal bath” of particles. This effect is well known and called the Unruh effect, and is an analog of Hawking radiation in space with zero curvature. Thus, the Minkowski vacuum looks like a heated medium from the point of view of an accelerated observer, and the natural goal is to study the properties of such a medium in more detail. We show that if the Minkwoski vacuum is cooled, and we achieve a temperature below the Unruh temperature, then a phase transition occurs associated with the “fall beyond the horizon” of the lower Matsubara modes. This transition has many remarkable features, for example, for massless particles it is “polynomial,” and is also associated with the breaking of conformal symmetry.

We construct the hydrodynamic expansion for a rotating and accelerated medium in a curved space-time, and establish the relationship between the currents generated by the cosmological constant and the acceleration. Then we consider the more general case with a nonzero Weyl tensor, and show the duality between the current in flat space-time and the gravitational axial anomaly. This generalizes the previous derivation to the case with a nonzero Ricci tensor. Published by the American Physical Society 2024

We consider an accelerated relativistic fluid in four-dimensional (anti–)de Sitter space-time. Analyzing only hydrodynamic equations, we construct the equilibrium stress-energy tensor. We confirm that (A)dS vacuum corresponds to a thermal bath in the accelerated frame with a temperature, depending on the acceleration in a flat higher-dimensional (namely, five-dimensional) space, in which curved space-times are embedded. We develop the duality between hydrodynamics and gravity finding a direct relationship between the transport coefficients in flat and curved space-times.

Classical analogs of chiral vortical and magnetic effects, generated by the currents possessing the hydrodynamical helicity are considered. The earlier found phenomenon of helicity separation in heavy-ion collisions leads to the appearance of currents of opposite signs at the different sides of reaction plane, accompanied by the current parallel to the plane. We discuss briefly relation between classical and quantum chiral effects.