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

Master Thesis

2017

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http://hdl.handle.net/11427/27284
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thesis_sci_2017_grant_stuart_alastair.pdf (2.38 MB)
Authors
Grant-Stuart, Alastair
Supervisors
Murugan, Jeffrey
Shock, Jonathan
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University of Cape Town

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Department of Mathematics and Applied Mathematics
Faculty
Faculty of Science
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Abstract
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.
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Applied Mathematics

Reference:

Grant-Stuart, A. 2017. Entanglement entropy, the Ryu-Takayanagi prescription, and conformal maps. University of Cape Town.

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