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