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Born Geometry

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dc.contributor.authorSvoboda, David
dc.date.accessioned2020-04-21T15:56:55Z
dc.date.available2020-04-21T15:56:55Z
dc.date.issued2020-04-21
dc.date.submitted2020-03-24
dc.description.abstractIn this thesis, we summarize the work which we authored or co-authored during our PhD studies and also present additional details and ideas that are not found elsewhere. The main topic is the study of T-duality in theoretical physics through the lens of para-Hermitian geometry and Born geometry as well as the description of mathematical aspects of said geometries. In the summary portion, we introduce the D-bracket and a related notion of torsion on para-Hermitian manifolds, consequently using these geometric elements to define a unique connection with canonical properties analogous to the Levi-Civita connection in Riemannian geometry. We then discuss para-Hermitian geometry and Born geometry in the framework of generalized geometry, showing that both arise naturally in this context. We also show that the D-bracket can be recovered from the small and large Courant algebroids of the para-Hermitian manifold using the formalism of generalized geometry. Lastly, we discuss applications to theoretical physics beyond the immediate context of T-duality, showing that our generalized-geometric formulations of para-Hermitian geometry and Born geometry correspond to extended symmetries of two-dimensional non-linear sigma models. We also introduce the notion of para-Calabi-Yau manifolds and use this new geometry to study the semi-flat mirror symmetry. We show, in particular, that both the mirror manifolds carry Born structures and that the mirror map relates the symplectic moduli space of the Born geometry on one side to the complex and para-complex moduli on the other side. Additionally, we discuss the para-Hermitian geometry underlying the topological T-duality of Bouwknegt, Evslin and Mathai and present various new discussions and reformulations of known results.en
dc.identifier.urihttp://hdl.handle.net/10012/15772
dc.language.isoenen
dc.pendingfalse
dc.publisherUniversity of Waterlooen
dc.subjectBorn geometryen
dc.subjectpara-Hermitian geometryen
dc.subjectdifferential geometryen
dc.subjectgeneralized geometryen
dc.subjectstring theoryen
dc.subjectT-dualityen
dc.subjectCourant algebroiden
dc.subjectdouble field theoryen
dc.subjectsigma modelen
dc.subjectCalabi-Yauen
dc.subjectpara-Calabi-Yauen
dc.subjectmirror symmetryen
dc.titleBorn Geometryen
dc.typeDoctoral Thesisen
uws-etd.degreeDoctor of Philosophyen
uws-etd.degree.departmentPhysics and Astronomyen
uws-etd.degree.disciplinePhysicsen
uws-etd.degree.grantorUniversity of Waterlooen
uws.contributor.advisorMoraru, Ruxandra
uws.contributor.advisorFreidel, Laurent
uws.contributor.affiliation1Faculty of Scienceen
uws.peerReviewStatusUnrevieweden
uws.published.cityWaterlooen
uws.published.countryCanadaen
uws.published.provinceOntarioen
uws.scholarLevelGraduateen
uws.typeOfResourceTexten

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