Chiral vortical effect: Black-hole versus flat-space derivation

G Yu Prokhorov,O V Teryaev,V I Zakharov

doi:10.1103/physrevd.102.121702

Abstract

The chiral vortical effect (CVE) was derived first for non-interacting massless fermions. Recently, an alternative derivation of the CVE was suggested which relates it to the radiation from the horizon of a rotating black hole. We attempt to generalize the latter derivation to the case of photons and encounter a crucial factor of two difference between the two ways of visualizing the CVE. Reservations and possible explanations are briefly discussed.

Highlights

Joint Institute for Nuclear Research, Joliot-Curie Street 6, Dubna 141980, Russia and Institute of Theoretical and Experimental Physics, NRC Kurchatov Institute, Bolshaya Cheremushkinskaya 25, Moscow 117218, Russia
The chiral vortical effect (CVE) grows as S3, while the flat-space relations result in a dependence which is linear in S
The chiral gravitational anomalies for spin-1=2 and spin-1 massless particles are proportional to the same RR, and the effect of the rotating black hole reduces to a universal geometric factor

Summary

GRAVITATIONAL CHIRAL ANOMALY AND CVE FOR PHOTONS

1 pffi−ffiffiffigffiffi εμνρσ Aν ∂ ρ Aσ ; ð2:1Þ where Aμ is the electromagnetic potential. There exists [11,12,13,14] the bosonic chiral gravitational anomaly h∇μKμi. Eq (2.3) suffices to evaluate the chiral vortical effect for photons in terms of the black-hole physics following the logic of Ref. The chiral gravitational anomalies for spin-1=2 and spin-1 massless particles are proportional to the same RR , and the effect of the rotating black hole reduces to a universal geometric factor. We are interested in the spin dependence of the chiral vortical effect. To elucidate the spin dependence of the CVE, it is convenient to compare fermionic and bosonic fields with an equal number of chiral degrees of freedom—that is, we normalize the photonic case to the case of a Weyl spinor. The problem is that the flat-space derivation suggests rather that the ratio (2.4) is equal to 2, not 4

Kubo-type relation

CVE from the Sommerfeld expansion

Limit of large spin of massless particles

Derivation of the Unruh temperature within the statistical approach

Coupling of acceleration and vorticity to the spin

CONCLUSIONS