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:	Victor E. Ambrus, Elizabeth Winstanley
Formato:	article
Lenguaje:	EN
Publicado:	MDPI AG 2021
Materias:	anti-de Sitter space dirac fermions finite temperature field theory rigid rotation chiral vortical effect Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/0bd05d8aef64465b99f65f649eb0521d
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spelling	oai:doaj.org-article:0bd05d8aef64465b99f65f649eb0521d2021-11-25T19:06:05ZVortical Effects for Free Fermions on Anti-De Sitter Space-Time10.3390/sym131120192073-8994https://doaj.org/article/0bd05d8aef64465b99f65f649eb0521d2021-10-01T00:00:00Zhttps://www.mdpi.com/2073-8994/13/11/2019https://doaj.org/toc/2073-8994Here, 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>.Victor E. AmbrusElizabeth WinstanleyMDPI AGarticleanti-de Sitter spacedirac fermionsfinite temperature field theoryrigid rotationchiral vortical effectMathematicsQA1-939ENSymmetry, Vol 13, Iss 2019, p 2019 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	anti-de Sitter space dirac fermions finite temperature field theory rigid rotation chiral vortical effect Mathematics QA1-939
spellingShingle	anti-de Sitter space dirac fermions finite temperature field theory rigid rotation chiral vortical effect Mathematics QA1-939 Victor E. Ambrus Elizabeth Winstanley Vortical Effects for Free Fermions on Anti-De Sitter Space-Time
description	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>.
format	article
author	Victor E. Ambrus Elizabeth Winstanley
author_facet	Victor E. Ambrus Elizabeth Winstanley
author_sort	Victor E. Ambrus
title	Vortical Effects for Free Fermions on Anti-De Sitter Space-Time
title_short	Vortical Effects for Free Fermions on Anti-De Sitter Space-Time
title_full	Vortical Effects for Free Fermions on Anti-De Sitter Space-Time
title_fullStr	Vortical Effects for Free Fermions on Anti-De Sitter Space-Time
title_full_unstemmed	Vortical Effects for Free Fermions on Anti-De Sitter Space-Time
title_sort	vortical effects for free fermions on anti-de sitter space-time
publisher	MDPI AG
publishDate	2021
url	https://doaj.org/article/0bd05d8aef64465b99f65f649eb0521d
work_keys_str_mv	AT victoreambrus vorticaleffectsforfreefermionsonantidesitterspacetime AT elizabethwinstanley vorticaleffectsforfreefermionsonantidesitterspacetime
_version_	1718410259005964288

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

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