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Vertex Algebras and Factorization Algebras

dc.contributor.advisorTeichner, Peter
dc.contributor.authorBrügmann, Daniel Georg
dc.date.accessioned2021-07-19T11:25:15Z
dc.date.available2021-07-19T11:25:15Z
dc.date.issued19.07.2021
dc.identifier.urihttps://hdl.handle.net/20.500.11811/9226
dc.description.abstractThis thesis is about the relationship between vertex algebras and Costello-Gwilliam factorization algebras, two mathematical approaches to chiral conformal field theory. Many vertex algebras have already been constructed. Some of these are known to arise from holomorphic factorization algebras on the plane of complex numbers. We prove that every Z-graded vertex algebra arises from such a factorization algebra.
First, we show that a Z-graded vertex algebra is the same thing as a geometric vertex algebra. Geometric vertex algebras serve as an intermediary between Z-graded vertex algebras and factorization algebras. Our factorization algebras take values in the symmetric monoidal category of complete bornological vector spaces. We describe how to obtain geometric vertex algebras from certain prefactorization algebras with values in the symmetric monoidal category of complete bornological vector spaces. Second, we attach a prefactorization algebra FV to every geometric vertex algebra and show that the geometric vertex algebra associated with FV is isomorphic to V. Third, we prove that FV is in fact a factorization algebra.
en
dc.language.isoeng
dc.rightsIn Copyright
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/
dc.subjectVertexalgebren
dc.subjectChirale Konforme Feldtheorie
dc.subjectFaktorisierungsalgebren
dc.subjectQuantenfeldtheorie
dc.subjectBornologische Vektorräume
dc.subjectKomplexe Analysis
dc.subjectvertex algebras
dc.subjectchiral conformal field theory
dc.subjectfactorization algebras
dc.subjectquantum field theory
dc.subjectbornological vector spaces
dc.subjectcomplex analysis
dc.subject.ddc510 Mathematik
dc.titleVertex Algebras and Factorization Algebras
dc.typeDissertation oder Habilitation
dc.publisher.nameUniversitäts- und Landesbibliothek Bonn
dc.publisher.locationBonn
dc.rights.accessRightsopenAccess
dc.identifier.urnhttps://nbn-resolving.org/urn:nbn:de:hbz:5-62836
ulbbn.pubtypeErstveröffentlichung
ulbbnediss.affiliation.nameRheinische Friedrich-Wilhelms-Universität Bonn
ulbbnediss.affiliation.locationBonn
ulbbnediss.thesis.levelDissertation
ulbbnediss.dissID6283
ulbbnediss.date.accepted25.03.2021
ulbbnediss.instituteAngegliederte Institute, verbundene wissenschaftliche Einrichtungen : Max-Planck-Institut für Mathematik
ulbbnediss.fakultaetMathematisch-Naturwissenschaftliche Fakultät
dc.contributor.coRefereeHenriques, André
ulbbnediss.contributor.gnd107436547X
ulbbn.doiRequestnein


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