A Dissertation submitted to the Faculty of Science,
University of the Witwatersrand,
in fulfilment of the requirements for
the degree of Master of Science. 14 May 2013 / We study the action of the dilatation operator on restricted Schur polynomials labeled by Young diagrams
with p long columns or p long rows. A new version of Schur-Weyl duality provides a powerful approach
to the computation and manipulation of the symmetric group operators appearing in the restricted Schur
polynomials. Using this new technology, we are able to evaluate the action of the one loop dilatation
operator. The result has a direct and natural connection to the Gauss Law constraint for branes with a
compact world volume. Generalzing previous results, we find considerable evidence that the dilatation
operator reduces to a decoupled set of harmonic oscillators. This strongly suggests that integrability in
N = 4 super Yang-Mills theory is not just a feature of the planar limit, but extends to other large N but
non-planar limits.
| Identifer | oai:union.ndltd.org:netd.ac.za/oai:union.ndltd.org:wits/oai:wiredspace.wits.ac.za:10539/12923 |
| Date | 30 July 2013 |
| Creators | Mathwin, C. R. |
| Source Sets | South African National ETD Portal |
| Language | English |
| Detected Language | English |
| Type | Thesis |
| Format | application/pdf |
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