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 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.

Grantor dc:publisher.institution

Department of Mathematics and Applied Mathematics

Year dc:date.issued

2017

Author dc:creator

• Grant-Stuart, Alastair

Advisors dc:contributor.advisor

• Murugan, Jeffrey
• Shock, Jonathan

Language dc:language.iso

eng

Handle dc:identifier.uri

http://hdl.handle.net/11427/27284

OAI identifier oai:identifier

oai:open.uct.ac.za:11427/27284