A thesis submitted to the Faculty of Science, University of the Witwatersrand, Johannesburg, in fulfilment of the requirements for the degree of Doctor of Philosophy. February 2015. / We explore the non-perturbative physics of giant gravitons in type IIB string theory
on the AdS5 ⇥ S5 background in this thesis. The gauge theory dual is N = 4
super Yang-Mills theory with a U(N) gauge group. We diagonalise the one and
two-loop dilatation operators acting on the restricted Schur polynomial basis. These
operators are dual to a system of giant gravitons with strings attached. Hence, we
present evidence for integrability in certain non-planar sectors of the gauge theory.
In the second half of the thesis, we turn our focus to N = 4 super Yang-Mills
theory with an SO(N) gauge group. In this case, the geometry of the dual gravity
theory is AdS5 ⇥RP5. The non-planar physics of the SO(N) theory is distinct from
that of the U(N) theory. To pursue the goal of searching for non-planar integrability
in the SO(N) gauge theory, one might try to generalise the restricted Schur basis
to the SO(N) case. We propose such a basis and evaluate their two-point functions
exactly in the free theory. Further, we develop techniques to compute correlation
functions of multi-trace operators involving two scalar fields exactly. Lastly, we
extend these results to the theory with an Sp(N) gauge group.
| Identifer | oai:union.ndltd.org:netd.ac.za/oai:union.ndltd.org:wits/oai:wiredspace.wits.ac.za:10539/17661 |
| Date | 07 May 2015 |
| Creators | Kemp, Garreth James |
| Source Sets | South African National ETD Portal |
| Language | English |
| Detected Language | English |
| Type | Thesis |
| Format | application/pdf |
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