A dissertation submitted to the Faculty of Science, University of the Witwatersrand, Johannesburg, in fulfilment of requirements for the degree of Master of Science. Johannesburg, 2015. / The AdS/CFT correspondence asserts a duality between non-Abelian gauge theories
and quantum theories of gravity, established by the value of the gauge coupling
. Gerard t'Hooft found that the large N0 limit in non-Abelian Yang-Mills gauge
theories results in a planar diagram simpli cation of the topological expansion.
In this dissertation, SU(2) gauge theories are written in terms of vector models
(making use of collective eld theory to obtain an expression for the Jacobian),
a saddle point analysis is performed, and the large N limit taken. Initially this
procedure is done for gauge theories dimensionally reduced on T4 and R T3, and
then attempted for the full eld theory (without dimensional reduction). In each case
this results in an expression for the non-perturbative propagator. A nite volume
must be imposed to obtain a gap equation for the full eld theory; directives for
possible solutions to this di culty are discussed.
| Identifer | oai:union.ndltd.org:netd.ac.za/oai:union.ndltd.org:wits/oai:wiredspace.wits.ac.za:10539/18533 |
| Date | 05 1900 |
| Creators | Johnson, Celeste Irene |
| Source Sets | South African National ETD Portal |
| Language | English |
| Detected Language | English |
| Type | Thesis |
| Format | application/pdf |
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