Brane states and group representation theory
dc.contributor.author | Nokwara, Nkululeko | |
dc.date.accessioned | 2014-01-14T11:43:59Z | |
dc.date.available | 2014-01-14T11:43:59Z | |
dc.date.issued | 2014-01-14 | |
dc.description | A thesis submitted to the Faculty of Science, University of the Witwatersrand, in fulfilment of the requirements for the degree of Doctor of Philosophy. 3rd October 2013. | en_ZA |
dc.description.abstract | 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. | en_ZA |
dc.identifier.uri | http://hdl.handle.net10539/13470 | |
dc.language.iso | en | en_ZA |
dc.subject.lcsh | Quantum gravity. | |
dc.subject.lcsh | Yang-Mills theory. | |
dc.subject.lcsh | Polynomials. | |
dc.title | Brane states and group representation theory | en_ZA |
dc.type | Thesis | en_ZA |
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