Complex (super)-matrix models with external sources and q-ensembles of Chern–Simons and ABJ(M) type
Autor(a) principal: | |
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Data de Publicação: | 2020 |
Outros Autores: | |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
Texto Completo: | http://hdl.handle.net/10071/22960 |
Resumo: | The Langmann–Szabo–Zarembo (LSZ) matrix model is a complex matrix model with a quartic interaction and two external matrices. The model appears in the study of a scalar field theory on the non-commutative plane. We prove that the LSZ matrix model computes the probability of atypically large fluctuations in the Stieltjes–Wigert matrix model, which is a q-ensemble describing U(N) Chern–Simons theory on the three-sphere. The correspondence holds in a generalized sense: depending on the spectra of the two external matrices, the LSZ matrix model either describes probabilities of large fluctuations in the Chern–Simons partition function, in the unknot invariant or in the two-unknot invariant. We extend the result to supermatrix models, and show that a generalized LSZ supermatrix model describes the probability of atypically large fluctuations in the ABJ(M) matrix model. |
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Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
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7160 |
spelling |
Complex (super)-matrix models with external sources and q-ensembles of Chern–Simons and ABJ(M) typeRandom matrix ensemblesMatrix model formulation of gauge theoriesNon-commutative field theoryThe Langmann–Szabo–Zarembo (LSZ) matrix model is a complex matrix model with a quartic interaction and two external matrices. The model appears in the study of a scalar field theory on the non-commutative plane. We prove that the LSZ matrix model computes the probability of atypically large fluctuations in the Stieltjes–Wigert matrix model, which is a q-ensemble describing U(N) Chern–Simons theory on the three-sphere. The correspondence holds in a generalized sense: depending on the spectra of the two external matrices, the LSZ matrix model either describes probabilities of large fluctuations in the Chern–Simons partition function, in the unknot invariant or in the two-unknot invariant. We extend the result to supermatrix models, and show that a generalized LSZ supermatrix model describes the probability of atypically large fluctuations in the ABJ(M) matrix model.IOP Publishing2021-10-23T00:00:00Z2020-01-01T00:00:00Z20202021-07-22T14:53:55Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10071/22960eng1751-811310.1088/1751-8121/abb6b0Santilli, LeonardoTierz, M.info:eu-repo/semantics/openAccessreponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãoinstacron:RCAAP2023-11-09T17:59:49Zoai:repositorio.iscte-iul.pt:10071/22960Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T22:31:30.185204Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãofalse |
dc.title.none.fl_str_mv |
Complex (super)-matrix models with external sources and q-ensembles of Chern–Simons and ABJ(M) type |
title |
Complex (super)-matrix models with external sources and q-ensembles of Chern–Simons and ABJ(M) type |
spellingShingle |
Complex (super)-matrix models with external sources and q-ensembles of Chern–Simons and ABJ(M) type Santilli, Leonardo Random matrix ensembles Matrix model formulation of gauge theories Non-commutative field theory |
title_short |
Complex (super)-matrix models with external sources and q-ensembles of Chern–Simons and ABJ(M) type |
title_full |
Complex (super)-matrix models with external sources and q-ensembles of Chern–Simons and ABJ(M) type |
title_fullStr |
Complex (super)-matrix models with external sources and q-ensembles of Chern–Simons and ABJ(M) type |
title_full_unstemmed |
Complex (super)-matrix models with external sources and q-ensembles of Chern–Simons and ABJ(M) type |
title_sort |
Complex (super)-matrix models with external sources and q-ensembles of Chern–Simons and ABJ(M) type |
author |
Santilli, Leonardo |
author_facet |
Santilli, Leonardo Tierz, M. |
author_role |
author |
author2 |
Tierz, M. |
author2_role |
author |
dc.contributor.author.fl_str_mv |
Santilli, Leonardo Tierz, M. |
dc.subject.por.fl_str_mv |
Random matrix ensembles Matrix model formulation of gauge theories Non-commutative field theory |
topic |
Random matrix ensembles Matrix model formulation of gauge theories Non-commutative field theory |
description |
The Langmann–Szabo–Zarembo (LSZ) matrix model is a complex matrix model with a quartic interaction and two external matrices. The model appears in the study of a scalar field theory on the non-commutative plane. We prove that the LSZ matrix model computes the probability of atypically large fluctuations in the Stieltjes–Wigert matrix model, which is a q-ensemble describing U(N) Chern–Simons theory on the three-sphere. The correspondence holds in a generalized sense: depending on the spectra of the two external matrices, the LSZ matrix model either describes probabilities of large fluctuations in the Chern–Simons partition function, in the unknot invariant or in the two-unknot invariant. We extend the result to supermatrix models, and show that a generalized LSZ supermatrix model describes the probability of atypically large fluctuations in the ABJ(M) matrix model. |
publishDate |
2020 |
dc.date.none.fl_str_mv |
2020-01-01T00:00:00Z 2020 2021-10-23T00:00:00Z 2021-07-22T14:53:55Z |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/article |
format |
article |
status_str |
publishedVersion |
dc.identifier.uri.fl_str_mv |
http://hdl.handle.net/10071/22960 |
url |
http://hdl.handle.net/10071/22960 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
1751-8113 10.1088/1751-8121/abb6b0 |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.format.none.fl_str_mv |
application/pdf |
dc.publisher.none.fl_str_mv |
IOP Publishing |
publisher.none.fl_str_mv |
IOP Publishing |
dc.source.none.fl_str_mv |
reponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação instacron:RCAAP |
instname_str |
Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
instacron_str |
RCAAP |
institution |
RCAAP |
reponame_str |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
collection |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
repository.name.fl_str_mv |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
repository.mail.fl_str_mv |
|
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1799134876413198336 |