Vortical Effects for Free Fermions on Anti-De Sitter Space-Time

TL;DR

This paper investigates the behavior of free fermions in anti-de Sitter space under rotation, revealing curvature effects, validating the axial vortical effect, and analyzing volumetric properties and divergences at high rotation rates.

Contribution

It provides a geometric approach to compute thermal expectation values for fermions in AdS space and uncovers curvature effects and vortex phenomena in this setting.

Findings

Curvature introduces extra terms involving Ricci scalar R.

Axial vortical effect is validated in AdS space.

Divergences occur in total scalar condensate and energy as rotation approaches the inverse radius.

Abstract

Here, we study a quantum fermion field in rigid rotation at finite temperature on anti-de Sitter space. We assume that the rotation rate $\Omega$ is smaller than the inverse radius of curvature $\ell ^{-1}$, so that there is no speed of light surface and the static (maximally-symmetric) and rotating vacua coincide. This assumption enables us to follow a geometric approach employing a closed-form expression for the vacuum two-point function, which can then be used to compute thermal expectation values (t.e.v.s). In the high temperature regime, we find a perfect analogy with known results on Minkowski space-time, uncovering curvature effects in the form of extra terms involving the Ricci scalar $R$. The axial vortical effect is validated and the axial flux through two-dimensional slices is found to escape to infinity for massless fermions, while for massive fermions, it is completely converted into the pseudoscalar density $-i {\bar \psi} \gamma^5 \psi$. Finally, we discuss volumetric properties such as the total scalar condensate and the total energy within the space-time and show that they diverge as $[1 - \ell^2 \Omega^2]^{-1}$ in the limit $\Omega \rightarrow \ell ^{-1}$.