Dirac fermions on an anti-de Sitter background

Winstanley

2021

Symmetry

Self Cite

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.

Section: Introductionmentioning

confidence: 99%

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

Winstanley

2021

Symmetry

Self Cite

“…What are the properties of these rigidly-rotating states? Preliminary answers to these questions were presented in [52,53]. Our purpose in this paper is to provide more comprehensive results for both massless and massive fermions on adS space-time.…”

Section: Introductionmentioning

confidence: 99%

Thermal expectation values of fermions on anti-de Sitter space-time

Winstanley

2017

Class. Quantum Grav.

Self Cite

Abstract. Making use of the symmetries of anti-de Sitter space-time, we derive an analytic expression for the bispinor of parallel transport, from which we construct in closed form the vacuum Feynman Green's function of the Dirac field on this background. Using the imaginary time anti-periodicity property of the thermal Feynman Green's function, we calculate the thermal expectation values of the fermion condensate and stress-energy tensor and highlight the effect of quantum corrections as compared to relativistic kinetic theory results.

“…The first three nonzero coefficients in the series (45) of pressure of the ring as a function of the (inverse) normalized radius 1/L. The direction of the thermodynamic limit is shown by the arrow.…”

Section: Analytical Continuation: the Disk Of Analyticitymentioning

confidence: 99%

Rigidly-rotating quantum thermal states in bounded systems

The Fifteenth Marcel Grossmann Meeting

2022

The thermodynamics of rigidly rotating systems experience divergences when the system dimensions transverse to the rotation axis exceed the critical size imposed by the causality constraint. The rotation with imaginary angular frequency, suitable for numerical lattice simulations in Euclidean imaginary-time formalism, experiences fractalization of thermodynamics in the thermodynamic limit, when the system's pressure becomes a fractal function of the rotation frequency. Our work connects two phenomena by studying how thermodynamics fractalizes as the system size grows. We examine an analytically-accessible system of rotating massless scalar matter on a one-dimensional ring and the numerically treatable case of rotation in the cylindrical geometry and show how the ninionic deformation of statistics emerges in these systems. We discuss a no-go theorem on analytical continuation between real-and imaginary-rotating theories. Finally, we compute the moment of inertia and shape deformation coefficients caused by the rotation of the relativistic bosonic gas.