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 Ω is smaller than the inverse radius of curvature ℓ−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 −iψ¯γ5ψ. 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−ℓ2Ω2]−1 in the limit Ω→ℓ−1.
Highlights
One of the deepest and most fundamental results of quantum field theory in curved space-time is the Unruh effect [1,2,3,4,5]
In this paper we have studied the properties of rotating vacuum and thermal states for free fermions on anti-de Sitter (adS)
We restricted our attention to the case when the rotation rate is sufficiently small that no SLS forms. This enabled us to exploit the maximal symmetry of the underlying space-time and use a geometric approach to find the vacuum and thermal two-point functions
Summary
One of the deepest and most fundamental results of quantum field theory in curved space-time is the Unruh effect [1,2,3,4,5]. Considering first a quantum scalar field, rigidly-rotating thermal states are ill-defined everywhere in unbounded Minkowski space-time [19,22]. Regular rigidly-rotating thermal states exist for both boson and fermion fields if, instead of considering the whole of Minkowski space-time, a space-time region inside a cylindrical boundary is studied. For a quantum scalar field, applying either Dirichlet [28,34,35,36] or Neumann [28,34,37] boundary conditions yields a global vacuum state which, like the global Minkowski vacuum, respects the maximal symmetry of the underlying adS space-time. For a quantum scalar field, as on Minkowski space-time, the rotating and nonrotating vacua coincide [51], irrespective of whether or not there is an SLS.
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