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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
first_indexed 2025-04-03T15:25:10Z
last_indexed 2025-04-04T05:16:26Z
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recordtype RisThesis
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spelling 2025-04-03T16:27:24.0614243 v2 69223 2025-04-03 Applications of Chern-Simons Theories to Integrable Sigma Models 8bfb09eb5004a26277b2d08fd23116bb LEWIS COLE LEWIS COLE true false 2025-04-03 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. E-Thesis Swansea University, Wales, UK Integrability, sigma models, Chern-Simons theory, twistor theory 14 11 2024 2024-11-14 10.23889/SUThesis.69223 COLLEGE NANME COLLEGE CODE Swansea University Thompson, D. C. Doctoral Ph.D EPSRC, STFC EPSRC, STFC 2025-04-03T16:27:24.0614243 2025-04-03T16:11:56.6305805 Faculty of Science and Engineering School of Biosciences, Geography and Physics - Physics LEWIS COLE 1 69223__33942__0de7286967e542d5befaad3dc331c3dd.pdf 2024_Cole_L.final.69223.pdf 2025-04-03T16:24:31.8516953 Output 2130762 application/pdf E-Thesis – open access true Copyright: The Author, Lewis T. Cole, 2024 Distributed under the terms of a Creative Commons Attribution 4.0 License (CC BY 4.0) true eng https://creativecommons.org/licenses/by/4.0/
title Applications of Chern-Simons Theories to Integrable Sigma Models
spellingShingle Applications of Chern-Simons Theories to Integrable Sigma Models
LEWIS COLE
title_short Applications of Chern-Simons Theories to Integrable Sigma Models
title_full Applications of Chern-Simons Theories to Integrable Sigma Models
title_fullStr Applications of Chern-Simons Theories to Integrable Sigma Models
title_full_unstemmed Applications of Chern-Simons Theories to Integrable Sigma Models
title_sort Applications of Chern-Simons Theories to Integrable Sigma Models
author_id_str_mv 8bfb09eb5004a26277b2d08fd23116bb
author_id_fullname_str_mv 8bfb09eb5004a26277b2d08fd23116bb_***_LEWIS COLE
author LEWIS COLE
author2 LEWIS COLE
format E-Thesis
publishDate 2024
institution Swansea University
doi_str_mv 10.23889/SUThesis.69223
college_str Faculty of Science and Engineering
hierarchytype
hierarchy_top_id facultyofscienceandengineering
hierarchy_top_title Faculty of Science and Engineering
hierarchy_parent_id facultyofscienceandengineering
hierarchy_parent_title Faculty of Science and Engineering
department_str School of Biosciences, Geography and Physics - Physics{{{_:::_}}}Faculty of Science and Engineering{{{_:::_}}}School of Biosciences, Geography and Physics - Physics
document_store_str 1
active_str 0
description 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.
published_date 2024-11-14T05:27:36Z
_version_ 1851097828504371200
score 11.089386

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