A dissertation submitted in fulfillment of the requirements for the degree of Master of Science. August 2016. / The six scalar fields in N = 4 super Yang-Mills theory enjoy a global
SO(6) symmetry, and large N but non-planar limits of this theory are well-described
by adopting a group representation approach. Studies have shown
that the one-loop dilatation operator is highly determined by the action of
the su(2)=su(3) subalgebras on restricted Schur polynomials. These actions
involve the traces of products of projection operators. In this dissertation,
exact analytical formulae for these traces are found which in turn are used to find the exact action of these algebras on restricted Schur polynomials. The
potential of the su(2) algebra to determine the one-loop dilatation operator
is also explored. This is done by exploiting necessary symmetry conditions
and moving to a continuum limit in order to derive a number of partial differential
equations which determine the dilatation operator. The ultimate
goal of this work is to provide tools to find the exact one-loop dilatation
operator in the non-planar limit. / LG2017
| Identifer | oai:union.ndltd.org:netd.ac.za/oai:union.ndltd.org:wits/oai:wiredspace.wits.ac.za:10539/21663 |
| Date | January 2016 |
| Creators | Bornman, Nicholas |
| Source Sets | South African National ETD Portal |
| Language | English |
| Detected Language | English |
| Type | Thesis |
| Format | Online resource (84 pages), application/pdf |
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