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

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 $\Omega \rightarrow \ell ^{-1}$.