Chiral vortical effect in accelerated matter

P G Mitkin,V I Zakharov

doi:10.1103/physrevd.104.125011

Abstract

We revisit evaluation of the chiral vortical effect in accelerated matter. To first order in the acceleration the corresponding matrix element of the axial current can be reconstructed from its flat-space limit. A crucial point is existence of an extra conservation law of fluid helicity which is not related to the symmetry of the Lagrangian. As a result, one can reproduce, via the equivalence principle, the effect of the so-called gravimagnetic anomaly; resolving in this way a long standing puzzle of its interpretation. Moreover, as a consequence of the extra conservation law the microscopic axial charge and helicity of the macroscopic motion are separately conserved. Some further consequences from the matching of the equivalence principle with hydrodynamics concerning higher orders in gradient expansion or in the acceleration are briefly discussed.

Highlights

Chiral effects have attracted a lot of interest recently
For further details see the original paper [44]. In these notes we have considered an application of the equivalence principle to the ideal fluid hydrodynamics
We put an emphasis on the conservation laws inherent to ideal fluids, since the conservation laws are the backbone of the hydrodynamic approach

Summary

INTRODUCTION

Chiral effects have attracted a lot of interest recently. These effects can influence the dynamics of a variety of systems, from the interior of a neutron star and quark-gluon plasma to Weyl and Dirac semimetals (for a review see, e.g., [1,2]). The righthand side of (3) is of the fourth order in gradients and the corresponding current would be of the third order, while the CVE is of the first order, see (1) It was suggested, to interpret the generic temperature T as the Unruh temperature TU 1⁄4 a=ð2πÞ where a is the gravitational acceleration (for details see [13,15,16]). To interpret the generic temperature T as the Unruh temperature TU 1⁄4 a=ð2πÞ where a is the gravitational acceleration (for details see [13,15,16]) This substitution eliminates two of the gradients of the gravitational field in the hydrodynamic picture and allows to link the T2 part of the CVE to the anomaly (3).

CONSERVATION LAWS FOR IDEAL FLUIDS

TURNING ON GRAVITY

MATCHING THE EQUIVALENCE PRINCIPLE AND THERMODYNAMICS

DISCUSSION