Moss, Richard Treeve (1997) Aspects of duality. University of Southampton, Doctoral Thesis.
Abstract
In this thesis we study some possible extensions of a symmetry well known in string theory; T-duality. In string theory this symmetry maps local and topological features of the model. In considering other applications of these methods it is essential to ensure that we explore the topological properties of the system carefully.
We first consider an application in solid state physics; the quantum Hall effect. Here we have a three dimensional system with a two dimensional boundary. Understanding the interplay between the bulk and edge of the manifold allows us to identify the physical currents in a systematic manner. We find a quantised Hall conductivity described by the momentum and a topological label. Careful application of duality then leads to a dual model where the momentum and topological labels are interchanged. The extension of this to several fields is considered and a general dual model is constructed.
In the second section we go on to discuss the extension of T-duality to four dimensions. Once again we have to treat the topological aspects of the model with care and find a dual model which involves an antisymmetric tensor field. This result is then considered in the context of non-linear sigma models and the Skyrme model.
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