Vertex Algebras and Factorization Algebras
Vertex Algebras and Factorization Algebras
dc.contributor.advisor | Teichner, Peter | |
dc.contributor.author | Brügmann, Daniel Georg | |
dc.date.accessioned | 2021-07-19T11:25:15Z | |
dc.date.available | 2021-07-19T11:25:15Z | |
dc.date.issued | 19.07.2021 | |
dc.identifier.uri | https://hdl.handle.net/20.500.11811/9226 | |
dc.description.abstract | This 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.iso | eng | |
dc.rights | In Copyright | |
dc.rights.uri | http://rightsstatements.org/vocab/InC/1.0/ | |
dc.subject | Vertexalgebren | |
dc.subject | Chirale Konforme Feldtheorie | |
dc.subject | Faktorisierungsalgebren | |
dc.subject | Quantenfeldtheorie | |
dc.subject | Bornologische Vektorräume | |
dc.subject | Komplexe Analysis | |
dc.subject | vertex algebras | |
dc.subject | chiral conformal field theory | |
dc.subject | factorization algebras | |
dc.subject | quantum field theory | |
dc.subject | bornological vector spaces | |
dc.subject | complex analysis | |
dc.subject.ddc | 510 Mathematik | |
dc.title | Vertex Algebras and Factorization Algebras | |
dc.type | Dissertation oder Habilitation | |
dc.publisher.name | Universitäts- und Landesbibliothek Bonn | |
dc.publisher.location | Bonn | |
dc.rights.accessRights | openAccess | |
dc.identifier.urn | https://nbn-resolving.org/urn:nbn:de:hbz:5-62836 | |
ulbbn.pubtype | Erstveröffentlichung | |
ulbbnediss.affiliation.name | Rheinische Friedrich-Wilhelms-Universität Bonn | |
ulbbnediss.affiliation.location | Bonn | |
ulbbnediss.thesis.level | Dissertation | |
ulbbnediss.dissID | 6283 | |
ulbbnediss.date.accepted | 25.03.2021 | |
ulbbnediss.institute | Angegliederte Institute, verbundene wissenschaftliche Einrichtungen : Max-Planck-Institut für Mathematik | |
ulbbnediss.fakultaet | Mathematisch-Naturwissenschaftliche Fakultät | |
dc.contributor.coReferee | Henriques, André | |
ulbbnediss.contributor.gnd | 107436547X |
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