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Chiral vortical effect is a generation of an axial current in the presence of the rotation.

On the one hand, the expression for the $\mathbf{CVE}$ has the following form: $$ \vec{J}^{5} = \vec \Omega \left( \frac{\mu^2}{4 \pi^2} + \frac{T^2}{12} \right) $$ where $\vec \Omega$ is the angular velocity, and $\mu$ is the chemical potential. This expression can be derived from the partition function directly: $$ \langle \vec{J}^{5} \rangle = \int \limits \frac{\varepsilon^2 d \varepsilon}{4 \pi^2} \left(\frac{1}{1 + e^{-\beta(\varepsilon - (\mu + \Omega/2))}} - \frac{1}{1 + e^{-\beta(\varepsilon - (\mu - \Omega/2))}} \right) $$ On the other hand, one says that the thermal part of $\mathbf{CVE}$ arises from the gravitational anomaly: $$ \nabla \cdot \vec{J}^{5} = \frac{1}{384 \pi^2} R_{\mu \nu \alpha \beta} \tilde{R}^{\mu \nu \alpha \beta} $$ And it claimed that both gravity and tempeature are universal. And there is even stronger statement:

Duality between statistical and gravitational approaches

My question is how to see the connection between gravity and temperature?

The finite temperature in Euclidean QFT is represented by a finite extent in the imaginary time direction, and imposing periodic(anti-periodic) conditions. And the non-zero graviational field would in some way deform our space, and the temporal extent, but is there more rigorous or general way to see the equivalence?

These questions are inspired by - https://indico.jinr.ru/event/1469/contributions/9896/attachments/8129/12120/zakharov_20_10_2020.pdf

This talk is given at a conference https://indico.jinr.ru/event/1469/timetable/#20201020 .

Slides are from the talk, given by Valentin Zakharov :

Polarization of elementary particles in heavy ion collisions as a manifestation of anomalies in quantum field theory

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Did you read my and Ji-Young Kim's derivation using the Kerr metric? https://arxiv.org/abs/1804.08668 ? I'd like to know what you think/

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  • $\begingroup$ very interesting, I'll have a look! $\endgroup$ Commented Oct 22, 2020 at 17:04
  • $\begingroup$ I've read your paper and It made rather a strong impression on me, but there are some points would like to clarify. Would you mind if I've contacted you and asked some questions? $\endgroup$ Commented Oct 25, 2020 at 7:01
  • $\begingroup$ Sure. E-mail me at the address on the paper. $\endgroup$
    – mike stone
    Commented Oct 25, 2020 at 11:32

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