Includes bibliographical references. / The gauge theory/gravity correspondence encompasses a variety of di_erent specific dualities. We investigate various topics in the context of Super–Yang- Mills/type IIB string theory and superconformal Chern-Simons-matter/type IIA string theory dualities. We carry out a rather extensive study of the type IIA AdS3_S3_S3_S1 Green- Schwarz superstring, up to quadratic order in fermions. We discuss issues related to fixing its _-symmetry and show the one-loop finiteness of two-point functions of bosonic fields. We then perform a Hamiltonian analysis and compare SU(2) string states with predictions from the conjectured Bethe equations. Furthermore, we show that, at least at tree-level, the two-body S-matrix is reflectionless. We then concern ourselves with extending Mikhailov’s construction of giant gravitons from holomorphic functions to include meromorphic functions, which lead to giants with non-trivial topologies in AdS5_S5. We explore what topological configurations giants, whose dynamics preserve a certain amount of supersymmetry, assume. We are particularly interested in solutions created by a localised modification of a set of intersecting spherical giant gravitons, as this seems the most tractable limit. We finally explore some aspects of holographic particle-vortex duality, in particular its realisation in the ABJM model and a possible relation to Maxwell duality in AdS4. We formulate a symmetric version of the transformation that acts as a self-duality, show how to embed it as an abelian duality in the (2+1)-dimensional, N = 6 super–Chern-Simons-matter theory that is the ABJM model, and speculate on a possible non-abelian extension.
| Identifer | oai:union.ndltd.org:netd.ac.za/oai:union.ndltd.org:uct/oai:localhost:11427/13216 |
| Date | January 2014 |
| Creators | Rughoonauth, Nitin |
| Contributors | Murugan, Jeffrey |
| Publisher | University of Cape Town, Faculty of Science, Department of Mathematics and Applied Mathematics |
| Source Sets | South African National ETD Portal |
| Language | English |
| Detected Language | English |
| Type | Doctoral Thesis, Doctoral, PhD |
| Format | application/pdf |
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