Vertex Algebras and Factorization Algebras
Vertex Algebras and Factorization Algebras
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DissertationDate of Exam
25.03.2021Date of Publication
19.07.2021Advisor
Teichner, PeterCo-Referee
Henriques, AndréMetadata
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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.
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.
Subjects
Vertexalgebren, Chirale Konforme Feldtheorie, Faktorisierungsalgebren, Quantenfeldtheorie, Bornologische Vektorräume, Komplexe Analysis, vertex algebras, chiral conformal field theory, factorization algebras, quantum field theory, bornological vector spaces, complex analysis
Classification (DDC)
510 MathematikBrügmann, Daniel Georg: Vertex Algebras and Factorization Algebras. - Bonn, 2021. - Dissertation, Rheinische Friedrich-Wilhelms-Universität Bonn.
Online-Ausgabe in bonndoc: https://nbn-resolving.org/urn:nbn:de:hbz:5-62836
Online-Ausgabe in bonndoc: https://nbn-resolving.org/urn:nbn:de:hbz:5-62836
@phdthesis{handle:20.500.11811/9226,
urn: https://nbn-resolving.org/urn:nbn:de:hbz:5-62836,
author = {{Daniel Georg Brügmann}},
title = {Vertex Algebras and Factorization Algebras},
school = {Rheinische Friedrich-Wilhelms-Universität Bonn},
year = 2021,
month = jul,
note = {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.},
url = {https://hdl.handle.net/20.500.11811/9226}
}
urn: https://nbn-resolving.org/urn:nbn:de:hbz:5-62836,
author = {{Daniel Georg Brügmann}},
title = {Vertex Algebras and Factorization Algebras},
school = {Rheinische Friedrich-Wilhelms-Universität Bonn},
year = 2021,
month = jul,
note = {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.},
url = {https://hdl.handle.net/20.500.11811/9226}
}
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