The goal of this thesis is to obtain a superfield formulation of local supersymmetry, and to construct via this formalism a model of spontaneous local supersymmetry breakdown. In the first chapter, the superfield method and some globally supersymmetric models are reviewed. These include Lagrangians for massive interacting chiral multiplets, and models for both massive and massless vector multiplets. In particular, the globally supersymmetric extension of the Higgs mechanism, due to Fayet, is described in detail. This model will form the basis of a locally supersymmetric model incorporating spontaneous supersymmetry breakdown in the third chapter. None of this work is original. The second chapter is devoted to gauging supersymmetry without superfields. The earliest supergravity theories (those not involving matter coupling) are reviewed. The fiber bundle approach is described, and shown to be ambiguous. An alternative algebraic scheme for dealing with gravitational symmetries is given. Superfield supergravity in two dimensions forms the subject matter of the third chapter. A brief glimpse of a one-dimensional locally supersymmetric theory (the spinning particle) is given. Its two-dimensional analogue, the spinning string, is obtained first without recourse to superfields, and then via an elegant superfield Ansatz due to Howe. It is shown how to derive this Ansatz and its transformation. Finally, a locally supersymmetric version of the Fayet model is given. The generalised Higgs mechanism works to remove the Goldstone spinor, but via a gauge field (the gravitino) which is forced to be non-dynamical in two dimensions. The methods of the third chapter are extended to four dimensions in the fourth chapter. The corresponding vielbein is derived, and shown not to transform covariantly without the addition of new terms. An attempt is made to find these terms, and it is argued that no additions can render the vielbein covariant. Consequently the approach of the third chapter proves inapplicable to four dimensions, and no matter-supergravity coupling can be obtained in this way. Three appendices on the history of anticommiting variables, the use of differential forms, and on some useful identities, complete the thesis.
| Identifer | oai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:649486 |
| Date | January 1979 |
| Creators | Derbes, David |
| Publisher | University of Edinburgh |
| Source Sets | Ethos UK |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
| Source | http://hdl.handle.net/1842/13625 |
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