Searching for self-duality in non-maximally supersymmetric backgrounds

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dc.contributor.advisorMurugan, Jeffreyen_ZA
dc.contributor.authorTarrant, Justine Aleciaen_ZA
dc.date.accessioned2017-06-06T09:35:27Z
dc.date.available2017-06-06T09:35:27Z
dc.date.issued2017en_ZA
dc.description.abstractFermionic T-duality is the generalisation to superspace of bosonic T-duality (i.e. to include fermionic degrees of freedom). Originally, T-duality described the equivalence relation between two physical theories, each living on a different background. However, this thesis is concerned with fermionic T-duality and its role in self-duality. The goal is to determine whether AdS backgrounds with less than maximal supersymmetry are self-dual. A background is said to be self-dual if, after a specific sequence of bosonic and fermionic T-duality transformations, the original background is recovered. Self-dual backgrounds are of great interest due to their link to integrability. Fermionic T-duality has played a pivotal role in proving that the maximally supersymmetric background AdS₅ × S⁵ is self-dual. This background is also known to be integrable, therefore, when it was shown to be self-dual, the hypothesis that self-duality implied integrability, and vice-versa, was born. We investigate how far this hypothesis may be stretched for a number of AdS backgrounds, for which integrability has already been determined. The following backgrounds were considered: AdS₂ × S² × T⁶ and AdSd × Sᵈ XT(¹⁰⁻³ᵈ) (d = 2; 3). This question of self-duality was approached in two ways. In the first approach we show that these less supersymmetric backgrounds are self-dual by working with the supergravity fields and using the fermionic Buscher procedure derived by Berkovits and Maldacena. In the second approach, we verify the self-duality of Green-Schwarz supercoset σ-models on AdSd × Sᵈ (d = 2; 3) backgrounds. Furthermore, we prove the self-duality of AdS₅ × S⁵ without gauge fixing K-symmetry. We show that self-duality is a property which holds for the exceptional backgrounds, where the need to T-dualise along one of the spheres arises, again. Nature is not supersymmetric, therefore learning how to do physics in AdS₅ × S⁵ is not enough. In order to understand theories like Quantum Chromodynamics, we need to systematically break the supersymmetry present in our toy models. In this regard, it is easy to appreciate the significance of studying backgrounds with less than maximal supersymmetry.en_ZA
dc.identifier.apacitationTarrant, J. A. (2017). <i>Searching for self-duality in non-maximally supersymmetric backgrounds</i>. (Thesis). University of Cape Town ,Faculty of Science ,Department of Mathematics and Applied Mathematics. Retrieved from http://hdl.handle.net/11427/24482en_ZA
dc.identifier.chicagocitationTarrant, Justine Alecia. <i>"Searching for self-duality in non-maximally supersymmetric backgrounds."</i> Thesis., University of Cape Town ,Faculty of Science ,Department of Mathematics and Applied Mathematics, 2017. http://hdl.handle.net/11427/24482en_ZA
dc.identifier.citationTarrant, J. 2017. Searching for self-duality in non-maximally supersymmetric backgrounds. University of Cape Town.en_ZA
dc.identifier.ris TY - Thesis / Dissertation AU - Tarrant, Justine Alecia AB - Fermionic T-duality is the generalisation to superspace of bosonic T-duality (i.e. to include fermionic degrees of freedom). Originally, T-duality described the equivalence relation between two physical theories, each living on a different background. However, this thesis is concerned with fermionic T-duality and its role in self-duality. The goal is to determine whether AdS backgrounds with less than maximal supersymmetry are self-dual. A background is said to be self-dual if, after a specific sequence of bosonic and fermionic T-duality transformations, the original background is recovered. Self-dual backgrounds are of great interest due to their link to integrability. Fermionic T-duality has played a pivotal role in proving that the maximally supersymmetric background AdS₅ × S⁵ is self-dual. This background is also known to be integrable, therefore, when it was shown to be self-dual, the hypothesis that self-duality implied integrability, and vice-versa, was born. We investigate how far this hypothesis may be stretched for a number of AdS backgrounds, for which integrability has already been determined. The following backgrounds were considered: AdS₂ × S² × T⁶ and AdSd × Sᵈ XT(¹⁰⁻³ᵈ) (d = 2; 3). This question of self-duality was approached in two ways. In the first approach we show that these less supersymmetric backgrounds are self-dual by working with the supergravity fields and using the fermionic Buscher procedure derived by Berkovits and Maldacena. In the second approach, we verify the self-duality of Green-Schwarz supercoset σ-models on AdSd × Sᵈ (d = 2; 3) backgrounds. Furthermore, we prove the self-duality of AdS₅ × S⁵ without gauge fixing K-symmetry. We show that self-duality is a property which holds for the exceptional backgrounds, where the need to T-dualise along one of the spheres arises, again. Nature is not supersymmetric, therefore learning how to do physics in AdS₅ × S⁵ is not enough. In order to understand theories like Quantum Chromodynamics, we need to systematically break the supersymmetry present in our toy models. In this regard, it is easy to appreciate the significance of studying backgrounds with less than maximal supersymmetry. DA - 2017 DB - OpenUCT DP - University of Cape Town LK - https://open.uct.ac.za PB - University of Cape Town PY - 2017 T1 - Searching for self-duality in non-maximally supersymmetric backgrounds TI - Searching for self-duality in non-maximally supersymmetric backgrounds UR - http://hdl.handle.net/11427/24482 ER - en_ZA
dc.identifier.urihttp://hdl.handle.net/11427/24482
dc.identifier.vancouvercitationTarrant JA. Searching for self-duality in non-maximally supersymmetric backgrounds. [Thesis]. University of Cape Town ,Faculty of Science ,Department of Mathematics and Applied Mathematics, 2017 [cited yyyy month dd]. Available from: http://hdl.handle.net/11427/24482en_ZA
dc.language.isoengen_ZA
dc.publisher.departmentDepartment of Mathematics and Applied Mathematicsen_ZA
dc.publisher.facultyFaculty of Scienceen_ZA
dc.publisher.institutionUniversity of Cape Town
dc.subject.otherApplied Mathematicsen_ZA
dc.titleSearching for self-duality in non-maximally supersymmetric backgroundsen_ZA
dc.typeDoctoral Thesis
dc.type.qualificationlevelDoctoral
dc.type.qualificationnamePhDen_ZA
uct.type.filetypeText
uct.type.filetypeImage
uct.type.publicationResearchen_ZA
uct.type.resourceThesisen_ZA
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