A dissertation submitted to the Faculty of Science, University of the Witwatersrand,
Johannesburg in ful lment of the requirements for the degree of Master of Science. June 29, 2017. / In this dissertation we explore the connection between entanglement and geometry. Recent
work in the AdS/CFT correspondence has uncovered fascinating connections between quantum
information and geometry, suggesting that entanglement in the CFT results in the emergence of
spacetime in the bulk . We work in the 1/2 BPS sector of the duality between N = 4 super
Yang Mills on R x S3 and IIB string theory on AdS5 S5. We aim to test this connection by
calculating the Renyi entropies in the presence of 1/2 BPS operators heavy enough to deform
the background geometry. This allows us to calculate the entanglement of these operators via
the replica trick. The Ryu-Takayanagi formula relates this calculation to a minimal surface in the
dual supergravity geometry, thus allowing us to observe how the boundary entanglement affects
the bulk spacetime. We build a formula to calculate correlation functions of 1/2 BPS operators
on the Riemann sheet that arises from the replica trick. This is a recursive formula based on
group theory techniques. We demonstrate how the formula works for light operators and discuss
how it can be generalised to include heavy operators by considering symmetric groups of higher
order. / LG2018
| Identifer | oai:union.ndltd.org:netd.ac.za/oai:union.ndltd.org:wits/oai:wiredspace.wits.ac.za:10539/25112 |
| Date | January 2017 |
| Creators | Mathaba, Kagiso |
| Source Sets | South African National ETD Portal |
| Language | English |
| Detected Language | English |
| Type | Thesis |
| Format | Online resource (95 pages), application/pdf |
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