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Applications of Chern-Simons Theories to Integrable Sigma Models / LEWIS COLE

Swansea University Author: LEWIS COLE

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DOI (Published version): 10.23889/SUThesis.69223

Abstract

This thesis studies the applications of Chern-Simons theories to integrable sigma models. Until recently, finding new examples of integrability was challenging, and the origins of the Lax formalism remained mysterious. However, the recent discovery of four-dimensional and six-dimensional Chern-Simons...

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Published: Swansea University, Wales, UK 2024
Institution: Swansea University
Degree level: Doctoral
Degree name: Ph.D
Supervisor: Thompson, D. C.
URI: https://cronfa.swan.ac.uk/Record/cronfa69223
Abstract: This thesis studies the applications of Chern-Simons theories to integrable sigma models. Until recently, finding new examples of integrability was challenging, and the origins of the Lax formalism remained mysterious. However, the recent discovery of four-dimensional and six-dimensional Chern-Simons theories offers a new perspective on these topics, and allows for the systematic construction of novel integrable sigma models. This thesis discusses the extension of these formalisms to a wider set of the known integrable theories. We incorporate sectors of gravity, integrable deformations, and gauged models into the scope of six-dimensional Chern-Simons theory, leading to generalisations of four-dimensional Chern-Simons theory and novel integrable field theories. In a separate line of study, we consider the three-dimensional Chern-Simons approach to chiral bosons, showing how it is related to various two-dimensional approaches. This allows us to generalise the known two-dimensional approaches to include both non-Abelian fields and twisted chirality.
Keywords: Integrability, sigma models, Chern-Simons theory, twistor theory
College: Faculty of Science and Engineering
Funders: EPSRC, STFC

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