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dc.contributor.authorBittleston, Roland
dc.date.accessioned2022-01-12T06:10:15Z
dc.date.available2022-01-12T06:10:15Z
dc.date.submitted2022-08-02
dc.identifier.urihttps://www.repository.cam.ac.uk/handle/1810/332645
dc.description.abstractThis thesis details my work exploring connections between integrable systems and Chern-Simons theories. It is divided into two parts. The first concerns the application of 4d Chern-Simons theory to describe integrable models with boundary, while the second concerns relations between holomorphic Chern-Simons theory on twistor space, 4d Chern-Simons theory and the anti-self-dual Yang-Mills equations. Part one opens with a review of 4d Chern-Simons theory, including a discussion of its connections to both quantum and classical integrable systems. It then turns to the results of this thesis concerning the application of 4d Chern-Simons theory to generate solutions of the boundary Yang-Baxter equation. They include: defining the boundary analogue of a quasi-classical $R$-matrix and classical $r$-matrix; realising $K$-matrices as the vacuum expectation values of Wilson lines in 4d Chern-Simons theory on a $\bbZ_2$ orbifold; deriving the order $\hbar$ contribution to a $K$-matrix in the rational case and verifying that it obeys the boundary Yang-Baxter equation to second order in $\hbar$; determining the OPE of bulk and boundary Wilson lines; demonstrating that boundary line operators are labelled by representations of twisted Yangians; giving the gauge theory realisation of boundary unitarity and the Sklyanin determinant; proving the uniqueness of the rational $K$-matrix; obtaining explicit formulae for the order $\hbar$ contributions to trigonometric and elliptic $K$-matrices and matching them to examples in the literature. Part two begins with a review of twistor theory. This is followed by the results of this thesis concerning the connections between holomorphic Chern-Simons theory on twistor space, 4d Chern-Simons theory and the anti-self-dual Yang-Mills equations. They include: showing that holomorphic Chern-Simons theory on twistor space for a meromorphic measure descends to an integrable theory on 4d spacetime; extending these results to indefinite signatures; identifying 4d Chern-Simons theory as the quotient of a 6d Chern-Simons theory on twistor correspondence space by an appropriate lift of the 2d translation group on spacetime; quotienting holomorphic Chern-Simons theory on twistor space by a 1 dimensional group of translations to obtain a 5d Chern-Simons theory on minitwistor correspondence space describing the Bogomolny equations.
dc.rightsAll Rights Reserved
dc.rights.urihttps://www.rioxx.net/licenses/all-rights-reserved/
dc.subjectChern-Simons
dc.subjectIntegrability
dc.subjectTwistor
dc.subjectIntegrable
dc.titleIntegrability from Chern-Simons theories
dc.typeThesis
dc.type.qualificationlevelDoctoral
dc.type.qualificationnameDoctor of Philosophy (PhD)
dc.publisher.institutionUniversity of Cambridge
dc.date.updated2022-01-10T14:34:41Z
dc.identifier.doi10.17863/CAM.80090
rioxxterms.licenseref.urihttps://www.rioxx.net/licenses/all-rights-reserved/
rioxxterms.typeThesis
dc.publisher.collegeTrinity
pubs.funder-project-idEPSRC (1936254)
pubs.funder-project-idEngineering and Physical Sciences Research Council (1936254)
cam.supervisorSkinner, David
cam.supervisor.orcidSkinner, David [0000-0002-3014-9127]
cam.depositDate2022-01-10
pubs.licence-identifierapollo-deposit-licence-2-1
pubs.licence-display-nameApollo Repository Deposit Licence Agreement


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