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Thesis (Ph. D.)--University of Texas at Austin, 2002. / Vita. Includes bibliographical references. Available also from UMI Company.

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Gauge/gravity duality is an important tool for learning about strongly coupled gauge theories. This thesis explores a set of examples of this duality in which the field theories have SU(2|4) supersymmetry and discrete sets of vacuum solutions. Specifically, we use the duality to propose Lagrangian definitions of type IIA Little String Theory on S⁵ as double-scaling limits of the Plane-Wave Matrix Model, maximally supersymmetric Yang-Mills theory on R x S² and N=4 supersymmetric Yang-Mills theory on R×S³/Zk. We find the supergravity solutions dual to generic vacua of the Plane-Wave Matrix Model and maximally supersymmetric Yang-Mills theory on R×S². We use the supergravity duals to calculate new instanton amplitudes for the Plane-Wave Matrix Model at strong coupling. Finally, we study a natural coarse-graining of the vacua, and find that the associated geometries are singular. We define an entropy functional that vanishes for regular geometries, is non-zero for singular geometries, and is maximized by the thermal state.

We define a Yang-Mills model in 1+1 dimensions coupled to a real scalar field and we study the Yang-Mills flow equations for this simple model. Yang-Mills flows have not been thoroughly studied, especially in a physical context, but may be able to provide valuable insight into both particle physics as well as gravity. We study our model using both the Hamiltonian equations and Euler-Lagrange equations, and we calculate the flow numerically using a simple finite difference method for the case of an Abelian Lie group and static fields. We are able to find several analytic solutions to the equations of motion and the numerical calculation of the flow suggests most non-constant solutions are unstable. We also find that the flow depends upon the relative values of the coupling constant and the mass of the scalar field. The results found with this simple model provide a starting point for the study of Yang-Mills flow in the context of more complicated (but more physical) models such as the Abelian Higgs.

This thesis is concerned with the possible sums of perturbation series in mass- less, renormalizable field theories. It shows that, given a free choice of scheme, the limit of the sequence of approximants is arbitrary. Restricting the choice to finite schemes, in particular "zero schemes", yields a perturbatively unique limit to the sequence of approximants. An operational method for calculating perturbative expansions in the class of zero schemes is discussed. A comparison of various optimization schemes is given for a few phenomenological examples in QCD and QED.

Gauge/gravity duality is an important tool for learning about strongly coupled gauge theories. This thesis explores a set of examples of this duality in which the field theories have SU(2|4) supersymmetry and discrete sets of vacuum solutions. Specifically, we use the duality to propose Lagrangian definitions of type IIA Little String Theory on S⁵ as double-scaling limits of the Plane-Wave Matrix Model, maximally supersymmetric Yang-Mills theory on R x S² and N=4 supersymmetric Yang-Mills theory on R×S³/Zk. We find the supergravity solutions dual to generic vacua of the Plane-Wave Matrix Model and maximally supersymmetric Yang-Mills theory on R×S². We use the supergravity duals to calculate new instanton amplitudes for the Plane-Wave Matrix Model at strong coupling. Finally, we study a natural coarse-graining of the vacua, and find that the associated geometries are singular. We define an entropy functional that vanishes for regular geometries, is non-zero for singular geometries, and is maximized by the thermal state.

Thesis (Ph. D.)--University of Adelaide, Dept. of Physics and Mathematical Physics, 1992. / Includes bibliographical references (leaves 117-120).

Thesis (Ph.D.)--Hong Kong University of Science and Technology, 2008. / Includes bibliographical references (p. 123-131). Also available in electronic version.