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Entanglement entropy, the Ryu-Takayanagi prescription, and conformal maps
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 n...
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| Format: | Thesis |
| Language: | English |
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Department of Mathematics and Applied Mathematics
2018
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| _version_ | 1867613271896358912 |
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| access_status_str | Open Access |
| author | Grant-Stuart, Alastair |
| author2 | Murugan, Jeffrey |
| author_browse | Grant-Stuart, Alastair Murugan, Jeffrey |
| author_facet | Murugan, Jeffrey Grant-Stuart, Alastair |
| author_sort | Grant-Stuart, Alastair |
| collection | Thesis |
| description | 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. |
| format | Thesis |
| id | oai:open.uct.ac.za:11427/27284 |
| institution | University of Cape Town (South Africa) |
| language | eng |
| last_indexed | 2026-06-10T12:33:28.738Z |
| license_str | Not specified — see source repository |
| provenance_str_mv | Harvested via OAI-PMH from UCTD — University of Cape Town Open Access Repository |
| publishDate | 2018 |
| publishDateRange | 2018 |
| publishDateSort | 2018 |
| publisher | Department of Mathematics and Applied Mathematics |
| publisherStr | Department of Mathematics and Applied Mathematics |
| record_format | dspace |
| source_str | UCTD — University of Cape Town Open Access Repository |
| spelling | oai:open.uct.ac.za:11427/27284 Entanglement entropy, the Ryu-Takayanagi prescription, and conformal maps Grant-Stuart, Alastair Murugan, Jeffrey Shock, Jonathan Applied Mathematics 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. 2018-02-05T12:55:11Z 2018-02-05T12:55:11Z 2017 Master Thesis Masters MSc http://hdl.handle.net/11427/27284 eng application/pdf Department of Mathematics and Applied Mathematics Faculty of Science University of Cape Town |
| spellingShingle | Applied Mathematics Grant-Stuart, Alastair Entanglement entropy, the Ryu-Takayanagi prescription, and conformal maps |
| thesis_degree_str | Master's |
| title | Entanglement entropy, the Ryu-Takayanagi prescription, and conformal maps |
| title_full | Entanglement entropy, the Ryu-Takayanagi prescription, and conformal maps |
| title_fullStr | Entanglement entropy, the Ryu-Takayanagi prescription, and conformal maps |
| title_full_unstemmed | Entanglement entropy, the Ryu-Takayanagi prescription, and conformal maps |
| title_short | Entanglement entropy, the Ryu-Takayanagi prescription, and conformal maps |
| title_sort | entanglement entropy the ryu takayanagi prescription and conformal maps |
| topic | Applied Mathematics |
| url | http://hdl.handle.net/11427/27284 |
| work_keys_str_mv | AT grantstuartalastair entanglemententropytheryutakayanagiprescriptionandconformalmaps |