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Master of Science - Science / The giant graviton part of the AdS/CFT dictionary is expanded from consideration of N = 4 super Yang-Mills theory with U(N) gauge group to the case of an SU(N) gauge group. Candidate duals to giant gravitons for the U(N) case were found by Corley, Jevicki and Ramgoolam [4] to be Schur polynomials of the Lie algebra. In this dissertation, computational generalisation of the U(N) result is achieved, and a set of linearly independent operators in one-to-one correspondence with the half-BPS representations of the SU(N) gauge theory given. These tools allow the rst elucidation of bulk and boundary degrees of freedom via the dual eld theory, exploiting the usefulness of giant gravitons as probes of the geometry.

We develop noncommutative field theory, starting from a very basic background and explore recent and important results in classical noncommutative field theory. The background section is of interest because it presents mathematical and physical interpretations of differential geometry together in a coherent way, not seen in most of the literature. We present several interesting examples that resulted from recent research in the field.

The effective potential augments the classical potential with the quantum effects of virtual particles, and permits the study of spontaneous symmetry breaking. In contrast to the standard approach where the classical potential already leads to electroweak symmetry-breaking, the Coleman-Weinberg mechanism explores quantum corrections as the source of symmetry-breaking. This thesis explores extensions of the Coleman -Weinberg mechanism to the situations with more than one Higgs doublet. These multi-Higgs models have a long history , and occur most naturally in the Minimal Supersymmetric model. Mathematical foundations of the zeta function method will be developed and then applied to regularise the one-loop computation of the effective potentials in a model with two scalar fields.

The effective potential augments the classical potential with the quantum effects of virtual particles, and permits the study of spontaneous symmetry breaking. In contrast to the standard approach where the classical potential already leads to electroweak symmetry-breaking, the Coleman-Weinberg mechanism explores quantum corrections as the source of symmetry-breaking. This thesis explores extensions of the Coleman -Weinberg mechanism to the situations with more than one Higgs doublet. These multi-Higgs models have a long history , and occur most naturally in the Minimal Supersymmetric model. Mathematical foundations of the zeta function method will be developed and then applied to regularise the one-loop computation of the effective potentials in a model with two scalar fields.

Thesis (Ph. D.)--University of Texas at Austin, 2000. / Vita. Includes bibliographical references (leaves 126-135). Available also in a digital version from Dissertation Abstracts.

Thesis (Ph. D.)--University of Texas at Austin, 2003. / Supervisor: Willy Fischler. Vita. Includes bibliographical references. Also available from UMI.

Thesis (Ph. D.)--University of Chicago, Dept. of Geophysical Sciences, August 2003. / Includes bibliographical references. Also available on the Internet.

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