A renormalizable topological quantum field theory for gravity

Detalhes bibliográficos
Autor(a) principal: Sadovski, Guilherme Silva de Araújo
Data de Publicação: 2019
Tipo de documento: Tese
Idioma: eng
Título da fonte: Repositório Institucional da Universidade Federal Fluminense (RIUFF)
Texto Completo: https://app.uff.br/riuff/handle/1/9971
Resumo: In 1989 E. Witten, using traditional QFT techniques, develop an exact path integral representation to many classes of topological invariants. These QFTs, so-called Topological QFTs (TQFTs), share the property that all of their observables are metric-independent. In other words, the observables are global invariants classifying the topological and smooth structure of spacetime. In this sense, one could say, that TQFTs are examples of background independent and exactly soluble perturbative QFTs. One of the most proeminent example perhaps is the four dimensional Topological Yang-Mills theory (TYM). This theory can be obtained by the BRST quantization of the Pontryagin invariant ∫ Tr (FF), instead of the tradition Yang-Mills action ∫ Tr (F ⋆ F). The observables are known to be the Donaldson’s polynomials, which classify the smooth structure of the underlying manifold. In particular, TYM theory is so symmetric that it has remarkably simple quantum properties. For instance, in the Landau gauge, it renormalizes, to all orders in perturbation theory, with only one (nonphysical) parameter and the theory is actually exactly soluble at tree-level (all quantum corrections vanish). These remarkable properties led Witten to hypothesize if such a theory could describe an unbroken phase of General Relativity. In this thesis, we will propose a renormalizable TYM theory that can generate gravity via an explicity breaking of its topological BRST symmetry - thus fulfilling Witten’s vision. In particular, we will consider the family of Lovelock-Cartan theories of gravity due to their generality and closer relation to the gauge structure.
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spelling A renormalizable topological quantum field theory for gravityTeoria quântica de campos topológicaRenormalização (Física)Gravidade (Física)Gravidade quânticaProdução intelectualTeoria quântica de campos topológicaRenormalização (Física)Gravidade (Física)Gravidade quânticaProdução intelectualIn 1989 E. Witten, using traditional QFT techniques, develop an exact path integral representation to many classes of topological invariants. These QFTs, so-called Topological QFTs (TQFTs), share the property that all of their observables are metric-independent. In other words, the observables are global invariants classifying the topological and smooth structure of spacetime. In this sense, one could say, that TQFTs are examples of background independent and exactly soluble perturbative QFTs. One of the most proeminent example perhaps is the four dimensional Topological Yang-Mills theory (TYM). This theory can be obtained by the BRST quantization of the Pontryagin invariant ∫ Tr (FF), instead of the tradition Yang-Mills action ∫ Tr (F ⋆ F). The observables are known to be the Donaldson’s polynomials, which classify the smooth structure of the underlying manifold. In particular, TYM theory is so symmetric that it has remarkably simple quantum properties. For instance, in the Landau gauge, it renormalizes, to all orders in perturbation theory, with only one (nonphysical) parameter and the theory is actually exactly soluble at tree-level (all quantum corrections vanish). These remarkable properties led Witten to hypothesize if such a theory could describe an unbroken phase of General Relativity. In this thesis, we will propose a renormalizable TYM theory that can generate gravity via an explicity breaking of its topological BRST symmetry - thus fulfilling Witten’s vision. In particular, we will consider the family of Lovelock-Cartan theories of gravity due to their generality and closer relation to the gauge structure.Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)88f.NiteróiSobreiro, Rodrigo Ferreirahttp://lattes.cnpq.br/8162281947965514http://lattes.cnpq.br/2681651033373505Sadovski, Guilherme Silva de Araújo2019-06-12T19:51:17Z2019-06-12T19:51:17Z2019info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/doctoralThesisapplication/pdfSADOVSKI, Guilherme Silva de Araújo. A renormalizable topological quantum field theory for gravity. 2019. 88 f. Tese (Doutorado) - Universidade Federal Fluminense, Instituto de Física, Niterói, 2019.https://app.uff.br/riuff/handle/1/9971Aluno de DoutoradoopenAccesshttp://creativecommons.org/licenses/by-nc-nd/3.0/br/CC-BY-SAinfo:eu-repo/semantics/openAccessengreponame:Repositório Institucional da Universidade Federal Fluminense (RIUFF)instname:Universidade Federal Fluminense (UFF)instacron:UFF2020-07-27T17:11:48Zoai:app.uff.br:1/9971Repositório InstitucionalPUBhttps://app.uff.br/oai/requestriuff@id.uff.bropendoar:21202024-08-19T11:03:27.140152Repositório Institucional da Universidade Federal Fluminense (RIUFF) - Universidade Federal Fluminense (UFF)false
dc.title.none.fl_str_mv A renormalizable topological quantum field theory for gravity
title A renormalizable topological quantum field theory for gravity
spellingShingle A renormalizable topological quantum field theory for gravity
Sadovski, Guilherme Silva de Araújo
Teoria quântica de campos topológica
Renormalização (Física)
Gravidade (Física)
Gravidade quântica
Produção intelectual
Teoria quântica de campos topológica
Renormalização (Física)
Gravidade (Física)
Gravidade quântica
Produção intelectual
title_short A renormalizable topological quantum field theory for gravity
title_full A renormalizable topological quantum field theory for gravity
title_fullStr A renormalizable topological quantum field theory for gravity
title_full_unstemmed A renormalizable topological quantum field theory for gravity
title_sort A renormalizable topological quantum field theory for gravity
author Sadovski, Guilherme Silva de Araújo
author_facet Sadovski, Guilherme Silva de Araújo
author_role author
dc.contributor.none.fl_str_mv Sobreiro, Rodrigo Ferreira
http://lattes.cnpq.br/8162281947965514
http://lattes.cnpq.br/2681651033373505
dc.contributor.author.fl_str_mv Sadovski, Guilherme Silva de Araújo
dc.subject.por.fl_str_mv Teoria quântica de campos topológica
Renormalização (Física)
Gravidade (Física)
Gravidade quântica
Produção intelectual
Teoria quântica de campos topológica
Renormalização (Física)
Gravidade (Física)
Gravidade quântica
Produção intelectual
topic Teoria quântica de campos topológica
Renormalização (Física)
Gravidade (Física)
Gravidade quântica
Produção intelectual
Teoria quântica de campos topológica
Renormalização (Física)
Gravidade (Física)
Gravidade quântica
Produção intelectual
description In 1989 E. Witten, using traditional QFT techniques, develop an exact path integral representation to many classes of topological invariants. These QFTs, so-called Topological QFTs (TQFTs), share the property that all of their observables are metric-independent. In other words, the observables are global invariants classifying the topological and smooth structure of spacetime. In this sense, one could say, that TQFTs are examples of background independent and exactly soluble perturbative QFTs. One of the most proeminent example perhaps is the four dimensional Topological Yang-Mills theory (TYM). This theory can be obtained by the BRST quantization of the Pontryagin invariant ∫ Tr (FF), instead of the tradition Yang-Mills action ∫ Tr (F ⋆ F). The observables are known to be the Donaldson’s polynomials, which classify the smooth structure of the underlying manifold. In particular, TYM theory is so symmetric that it has remarkably simple quantum properties. For instance, in the Landau gauge, it renormalizes, to all orders in perturbation theory, with only one (nonphysical) parameter and the theory is actually exactly soluble at tree-level (all quantum corrections vanish). These remarkable properties led Witten to hypothesize if such a theory could describe an unbroken phase of General Relativity. In this thesis, we will propose a renormalizable TYM theory that can generate gravity via an explicity breaking of its topological BRST symmetry - thus fulfilling Witten’s vision. In particular, we will consider the family of Lovelock-Cartan theories of gravity due to their generality and closer relation to the gauge structure.
publishDate 2019
dc.date.none.fl_str_mv 2019-06-12T19:51:17Z
2019-06-12T19:51:17Z
2019
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
dc.type.driver.fl_str_mv info:eu-repo/semantics/doctoralThesis
format doctoralThesis
status_str publishedVersion
dc.identifier.uri.fl_str_mv SADOVSKI, Guilherme Silva de Araújo. A renormalizable topological quantum field theory for gravity. 2019. 88 f. Tese (Doutorado) - Universidade Federal Fluminense, Instituto de Física, Niterói, 2019.
https://app.uff.br/riuff/handle/1/9971
Aluno de Doutorado
identifier_str_mv SADOVSKI, Guilherme Silva de Araújo. A renormalizable topological quantum field theory for gravity. 2019. 88 f. Tese (Doutorado) - Universidade Federal Fluminense, Instituto de Física, Niterói, 2019.
Aluno de Doutorado
url https://app.uff.br/riuff/handle/1/9971
dc.language.iso.fl_str_mv eng
language eng
dc.rights.driver.fl_str_mv openAccess
http://creativecommons.org/licenses/by-nc-nd/3.0/br/
CC-BY-SA
info:eu-repo/semantics/openAccess
rights_invalid_str_mv openAccess
http://creativecommons.org/licenses/by-nc-nd/3.0/br/
CC-BY-SA
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Niterói
publisher.none.fl_str_mv Niterói
dc.source.none.fl_str_mv reponame:Repositório Institucional da Universidade Federal Fluminense (RIUFF)
instname:Universidade Federal Fluminense (UFF)
instacron:UFF
instname_str Universidade Federal Fluminense (UFF)
instacron_str UFF
institution UFF
reponame_str Repositório Institucional da Universidade Federal Fluminense (RIUFF)
collection Repositório Institucional da Universidade Federal Fluminense (RIUFF)
repository.name.fl_str_mv Repositório Institucional da Universidade Federal Fluminense (RIUFF) - Universidade Federal Fluminense (UFF)
repository.mail.fl_str_mv riuff@id.uff.br
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