Vortical Effects for Free Fermions on Anti-De Sitter Space-Time
Here, we study a quantum fermion field in rigid rotation at finite temperature on anti-de Sitter space. We assume that the rotation rate <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mo>Ω</mo></seman...
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| Autores principales: | , |
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| Formato: | article |
| Lenguaje: | EN |
| Publicado: |
MDPI AG
2021
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| Materias: | |
| Acceso en línea: | https://doaj.org/article/0bd05d8aef64465b99f65f649eb0521d |
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| Sumario: | Here, we study a quantum fermion field in rigid rotation at finite temperature on anti-de Sitter space. We assume that the rotation rate <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mo>Ω</mo></semantics></math></inline-formula> is smaller than the inverse radius of curvature <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mo>ℓ</mo><mrow><mo>−</mo><mn>1</mn></mrow></msup></semantics></math></inline-formula>, 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 <i>R</i>. 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 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>−</mo><mi>i</mi><mover accent="true"><mo>ψ</mo><mo>¯</mo></mover><msup><mo>γ</mo><mn>5</mn></msup><mo>ψ</mo></mrow></semantics></math></inline-formula>. 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 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mrow><mo>[</mo><mn>1</mn><mo>−</mo><msup><mo>ℓ</mo><mn>2</mn></msup><msup><mo>Ω</mo><mn>2</mn></msup><mo>]</mo></mrow><mrow><mo>−</mo><mn>1</mn></mrow></msup></semantics></math></inline-formula> in the limit <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>Ω</mo><mo>→</mo><msup><mo>ℓ</mo><mrow><mo>−</mo><mn>1</mn></mrow></msup></mrow></semantics></math></inline-formula>. |
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