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 gravi¬
tational symmetries is given.
Superfield supergravity in two dimensions forms the subject matter of
the third chapter. A brief glimpse of a one-dimensional locally supersym¬
metric 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 anticommuting variables, the use
of differential forms, and on some useful identities, complete the thesis.