Strings and solitons in gauge theories
Neil Turok · Spiral (Imperial College London) · 1983
This thesis covers two topics in nonabelian gauge theories.The first is the existence, in some spontaneously broken gauge theories of topologically stable 'string' solutions.A comprehensive classification of those grand unified theories yielding these solutions is given.The cosmological consequences of strings produced at the grand unification phase transition are investigated and it is shown how spinning loops of' string may lead to the formation of galaxies.The second topic is the connection between gauge theories and integrable systems, notably the Toda systems.These are known to possess soliton solutions, both topological and non-toplogical, and this fact is related in an essential way to their integrability.It is shown how self-dual gauge field configurations give rise to the Toda equations, and a complete classification of Toda systems is given.A new simple algebraic proof of the integrability of Toda systems is given which clarifies the role of an underlying 'Kac-Moody' algebra for the Toda lattice equations.This also gives a clue as to the quantisation of these systems, and a link with the 'Quantum Inverse Scattering'method.2.