Geometrical and nonperturbative aspects of low dimensional field theories

• Main Author: Murugan, Jeffrey
• Other Authors: Barashenkov, Igor
• Format: Dissertation
• Language: English
• Published: University of Cape Town 2014
• Subjects: Mathematics and Applied Maths
• Online Access: http://hdl.handle.net/11427/7681

Bibliography: leaves 84-88 === We present a collection of results on solitons in low-dimensional classical field theory. We begin by reviewing the geometrical setting of he nonlinear ơ-model and demonstrate the integrability of the theory in two-dimensions on a symmetric target manifold. After reviewing the construction of soliton solutions in the 0(3) ơ-model we consider a class of gauged nonlinear ơ-models on two-dimensional axially-symmetric target spaces. We show that, for a certain choice of self-interaction, these models are all self-dual and analyze the resulting Bogomol'nyi equations in the BPS limit using techniques from dynamical systems theory. Our analysis is then extended to topologically massive gauge fields. We conclude with a deviation into exploring links between four-dimensional self-dual Yang-Mills equations and various lower-dimensional field theories. In particular, we show that at the level of equations of motion, the Euclidean Yang-Mills equations in light-cone coordinates reduce to the two-dimensional nonlinear ơ-model.