Entanglement entropy, the Ryu-Takayanagi prescription, and conformal maps

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dc.contributor.advisorMurugan, Jeffreyen_ZA
dc.contributor.advisorShock, Jonathanen_ZA
dc.contributor.authorGrant-Stuart, Alastairen_ZA
dc.date.accessioned2018-02-05T12:55:11Z
dc.date.available2018-02-05T12:55:11Z
dc.date.issued2017en_ZA
dc.description.abstractWe define and explore the concepts underpinning the Ryu-Takayanagi prescription for entanglement entropy in a holographic theory. We begin by constructing entanglement entropy in finite-dimensional quantum systems, and defining the boundary at infinity of a bulk spacetime. This is sufficient for a naïve application of the Ryu-Takayanagi prescription to some simple examples; nonetheless, we review the general theory of minimal submanifolds in Riemannian ambient manifolds in order to better characterise the objects involved in the prescription. Finally, we explore the symmetries of the boundary theory to which the prescription applies, and thereby extend the aforementioned examples. Throughout, emphasis is placed on making explicit the mathematical structures that are taken for granted in the research literature.en_ZA
dc.identifier.apacitationGrant-Stuart, A. (2017). <i>Entanglement entropy, the Ryu-Takayanagi prescription, and conformal maps</i>. (Thesis). University of Cape Town ,Faculty of Science ,Department of Mathematics and Applied Mathematics. Retrieved from http://hdl.handle.net/11427/27284en_ZA
dc.identifier.chicagocitationGrant-Stuart, Alastair. <i>"Entanglement entropy, the Ryu-Takayanagi prescription, and conformal maps."</i> Thesis., University of Cape Town ,Faculty of Science ,Department of Mathematics and Applied Mathematics, 2017. http://hdl.handle.net/11427/27284en_ZA
dc.identifier.citationGrant-Stuart, A. 2017. Entanglement entropy, the Ryu-Takayanagi prescription, and conformal maps. University of Cape Town.en_ZA
dc.identifier.ris TY - Thesis / Dissertation AU - Grant-Stuart, Alastair AB - We define and explore the concepts underpinning the Ryu-Takayanagi prescription for entanglement entropy in a holographic theory. We begin by constructing entanglement entropy in finite-dimensional quantum systems, and defining the boundary at infinity of a bulk spacetime. This is sufficient for a naïve application of the Ryu-Takayanagi prescription to some simple examples; nonetheless, we review the general theory of minimal submanifolds in Riemannian ambient manifolds in order to better characterise the objects involved in the prescription. Finally, we explore the symmetries of the boundary theory to which the prescription applies, and thereby extend the aforementioned examples. Throughout, emphasis is placed on making explicit the mathematical structures that are taken for granted in the research literature. DA - 2017 DB - OpenUCT DP - University of Cape Town LK - https://open.uct.ac.za PB - University of Cape Town PY - 2017 T1 - Entanglement entropy, the Ryu-Takayanagi prescription, and conformal maps TI - Entanglement entropy, the Ryu-Takayanagi prescription, and conformal maps UR - http://hdl.handle.net/11427/27284 ER - en_ZA
dc.identifier.urihttp://hdl.handle.net/11427/27284
dc.identifier.vancouvercitationGrant-Stuart A. Entanglement entropy, the Ryu-Takayanagi prescription, and conformal maps. [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/11427/27284en_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.titleEntanglement entropy, the Ryu-Takayanagi prescription, and conformal mapsen_ZA
dc.typeMaster Thesis
dc.type.qualificationlevelMasters
dc.type.qualificationnameMScen_ZA
uct.type.filetypeText
uct.type.filetypeImage
uct.type.publicationResearchen_ZA
uct.type.resourceThesisen_ZA
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