Recent developments in string theory have led to the understanding that many physical systems posses multiple equivalent, or dual, descriptions which are distinguished by their usefulness in differing regions of parameter space. Dualities of this type often relate theories which exist in different numbers of space-time dimensions and it is the purpose of this thesis to examine several examples of this phenomenon. It is well known that the low energy dynamics of D3-branes is well described by N = 4 super-Yang-Mills theory in 3 + 1 dimensions. In the first part of this thesis it will be shown how the physics of magnetic monopole solutions of this theory is often best described by a 1 + 1 dimensional quantum field theory. In particular it is found that near the core of the monopole the most appropriate description of the physics is in terms of a particular version of non-commutative geometry arising from the non-abelian nature of the 1 + 1 dimensional field theory. The second part of this thesis discusses the duality between Anti de-Sitter Space and Conformal Field Theory (the AdS/CFT correspondence) which states that at strong coupling N = 4 Super-Yang-Mills theory is actually best described by type IIB superstring theory in 9 + 1 dimensions. The implications of this conjecture as applied to non-supersymmetric field theories are explored and it is found that many properties of quantum-chromo-dynamics (QCD) such as confinement and mass gaps can effectively be studied using string theory techniques. It is also shown how the mass spectra of glueballs in QCD-like theories can be computed. These techniques are then turned around to deduce from the field theory a perturbative proof of a positive energy conjecture for asymptotically AdS spaces.
| Identifer | oai:union.ndltd.org:LACETR/oai:collectionscanada.gc.ca:QMM.37881 |
| Date | January 2001 |
| Creators | Constable, Neil R. |
| Contributors | Myers, Robert C. (advisor) |
| Publisher | McGill University |
| Source Sets | Library and Archives Canada ETDs Repository / Centre d'archives des thèses électroniques de Bibliothèque et Archives Canada |
| Language | English |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
| Format | application/pdf |
| Coverage | Doctor of Philosophy (Department of Physics.) |
| Rights | All items in eScholarship@McGill are protected by copyright with all rights reserved unless otherwise indicated. |
| Relation | alephsysno: 001846406, proquestno: NQ75621, Theses scanned by UMI/ProQuest. |
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