ETD Collection

Permanent URI for this collectionhttps://wiredspace.wits.ac.za/handle/10539/104


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2014 - 20152

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Has files: YesSubject: search.filters.subject.Quantum gravity.

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    The simplest gauge-string duality
    (2015) Nkumane, Lwazi Khethukuthula
    The gauge/gravity correspondence is a conjectured exact duality between quantum eld theories and theories of quantum gravity. A very simple gauge/string duality, claims an equivalence between the Gaussian matrix model and the topological A-model string theory on P1. In this dissertation we study this duality, proposing concrete operators in the matrix model that are dual to gravitational descendants of the puncture operator of the topological string theory. We test our proposal by showing that a large number of matrix model correlators are in complete agreement with correlators in the dual topological string theory. Contact term interactions, as proposed by Gopakumar and Pius, play an interesting and non-trivial role in the duality.
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    Brane states and group representation theory
    (2014-01-14) Nokwara, Nkululeko
    A complete understanding of quantum gravity remains an open problem. However, the AdS/CFT correspondence which relates quantum eld theories that enjoy conformal symmetry to theories of (quantum) gravity is proving to be a useful tool in shedding light on this formidable problem. Recently developed group representation theoretic methods have proved useful in understanding the large N; but non-planar limit of N = 4 supersymmetric Yang-Mills theory. In this work, we study operators that are dual to excited giant gravitons, which corresponds to a sector of N = 4 super Yang-Mills theory that is described by a large N; but non-planar limit. After a brief review of the work done in the su (2) sector, we compute the spectrum of anomalous dimensions in the su (2) sector of the Leigh-Strassler deformed theory. The result resembles the spectrum of a shifted harmonic oscillator. We then explain how to construct restricted Schur polynomials built using both fermionic and bosonic elds which transform in the adjoint of the gauge group U (N) : We show that these operators diagonalise the free eld two point function to all orders in 1=N: As an application of our new operators, we study the action of the one-loop dilatation operator in the su (2,3) sector in a large N; but non-planar limit of N = 4 super Yang-Mills theory. As in the su (2) case, the resulting spectrum matches the spectrum of a set of decoupled oscillators. Finally, in an appendix, we study the action of the one-loop dilatation operator in an sl (2) sector of N = 4 super Yang-Mills theory. Again, the resulting spectrum matches that of a set of harmonic oscillators. In all these cases, we nd that the action of the dilatation operator is diagonalised by a double coset ansatz.