A dissertation submitted to the Faculty of Science, University of the
Witwatersrand, Johannesburg, in fulfilment of the requirements for the
degree of Master of Science. April 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. 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:10539/13018 |
| Date | 07 August 2013 |
| Creators | Dessein, Matthias |
| Source Sets | South African National ETD Portal |
| Language | English |
| Detected Language | English |
| Type | Thesis |
| Format | application/pdf |
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