{"@context":{"@vocab":"https://cir.nii.ac.jp/schema/1.0/","rdfs":"http://www.w3.org/2000/01/rdf-schema#","dc":"http://purl.org/dc/elements/1.1/","dcterms":"http://purl.org/dc/terms/","foaf":"http://xmlns.com/foaf/0.1/","prism":"http://prismstandard.org/namespaces/basic/2.0/","cinii":"http://ci.nii.ac.jp/ns/1.0/","datacite":"https://schema.datacite.org/meta/kernel-4/","ndl":"http://ndl.go.jp/dcndl/terms/","jpcoar":"https://github.com/JPCOAR/schema/blob/master/2.0/"},"@id":"https://cir.nii.ac.jp/crid/1363670319581651328.json","@type":"Article","productIdentifier":[{"identifier":{"@type":"DOI","@value":"10.1103/physrevd.77.126015"}},{"identifier":{"@type":"URI","@value":"http://link.aps.org/article/10.1103/PhysRevD.77.126015"}},{"identifier":{"@type":"URI","@value":"http://harvest.aps.org/v2/journals/articles/10.1103/PhysRevD.77.126015/fulltext"}},{"identifier":{"@type":"DOI","@value":"10.48550/arxiv.0802.2782"}}],"dc:title":[{"@value":"Fiber bundles and matrix models"}],"description":[{"notation":[{"@value":"We investigate relationship between a gauge theory on a principal bundle and that on its base space. In the case where the principal bundle is itself a group manifold, we also study relations of those gauge theories with a matrix model obtained by dimensionally reducing them to zero dimensions. First, we develop the dimensional reduction of Yang-Mills (YM) on the total space to YM-higgs on the base space for a general principal bundle. Second, we show a relationship that YM on an SU(2) bundle is equivalent to the theory around a certain background of YM-higgs on its base space. This is an extension of our previous work (hep-th/0703021), in which the same relationship concerning a U(1) bundle is shown. We apply these results to the case of $SU(n+1)$ as the total space. By dimensionally reducing YM on $SU(n+1)$, we obtain YM-higgs on $SU(n+1)/SU(n)\\simeq S^{2n+1}$ and on $SU(n+1)/(SU(n)\\times U(1))\\simeq CP^n$ and a matrix model. We show that the theory around each monopole vacuum of YM-higgs on $CP^n$ is equivalent to the theory around a certain vacuum of the matrix model in the commutative limit. By combing this with the relationship concerning a U(1) bundle, we realize YM-higgs on $SU(n+1)/SU(n)\\simeq S^{2n+1}$ in the matrix model. We see that the relationship concerning a U(1) bundle can be interpreted as Buscher's T-duality."}]},{"notation":[{"@value":"53 pages, references added, typos corrected"}]}],"creator":[{"@id":"https://cir.nii.ac.jp/crid/1383670319581651328","@type":"Researcher","foaf:name":[{"@value":"Takaaki Ishii"}]},{"@id":"https://cir.nii.ac.jp/crid/1383670319581651330","@type":"Researcher","foaf:name":[{"@value":"Goro Ishiki"}]},{"@id":"https://cir.nii.ac.jp/crid/1383670319581651331","@type":"Researcher","foaf:name":[{"@value":"Shinji Shimasaki"}]},{"@id":"https://cir.nii.ac.jp/crid/1383670319581651329","@type":"Researcher","foaf:name":[{"@value":"Asato Tsuchiya"}]}],"publication":{"publicationIdentifier":[{"@type":"PISSN","@value":"15507998"},{"@type":"EISSN","@value":"15502368"}],"prism:publicationName":[{"@value":"Physical Review D"}],"dc:publisher":[{"@value":"American Physical Society (APS)"}],"prism:publicationDate":"2008-06-20","prism:volume":"77","prism:number":"12","prism:startingPage":"126015"},"reviewed":"false","dcterms:accessRights":"http://purl.org/coar/access_right/c_abf2","dc:rights":["http://link.aps.org/licenses/aps-default-license"],"url":[{"@id":"http://link.aps.org/article/10.1103/PhysRevD.77.126015"},{"@id":"http://harvest.aps.org/v2/journals/articles/10.1103/PhysRevD.77.126015/fulltext"}],"createdAt":"2008-06-20","modifiedAt":"2019-05-12","foaf:topic":[{"@id":"https://cir.nii.ac.jp/all?q=High%20Energy%20Physics%20-%20Theory","dc:title":"High Energy Physics - Theory"},{"@id":"https://cir.nii.ac.jp/all?q=High%20Energy%20Physics%20-%20Theory%20(hep-th)","dc:title":"High Energy Physics - Theory (hep-th)"},{"@id":"https://cir.nii.ac.jp/all?q=FOS:%20Physical%20sciences","dc:title":"FOS: Physical sciences"}],"relatedProduct":[{"@id":"https://cir.nii.ac.jp/crid/1360004235012070912","@type":"Article","resourceType":"学術雑誌論文(journal article)","relationType":["isReferencedBy"],"jpcoar:relatedTitle":[{"@value":"Large-<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\"><mml:mi>N</mml:mi></mml:math>reduction for<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\"><mml:mi mathvariant=\"script\">N</mml:mi><mml:mo mathvariant=\"bold\">=</mml:mo><mml:mn>2</mml:mn></mml:math>quiver Chern-Simons theories on<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\"><mml:msup><mml:mi>S</mml:mi><mml:mn>3</mml:mn></mml:msup></mml:math>and localization in matrix models"}]},{"@id":"https://cir.nii.ac.jp/crid/1360004235036525952","@type":"Article","resourceType":"学術雑誌論文(journal article)","relationType":["isReferencedBy"],"jpcoar:relatedTitle":[{"@value":"Deconfinement Phase Transition in<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\"><mml:mi mathvariant=\"script\">N</mml:mi><mml:mo>=</mml:mo><mml:mn>4</mml:mn></mml:math>Super Yang-Mills Theory on<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\"><mml:mi>R</mml:mi><mml:mo>×</mml:mo><mml:msup><mml:mi>S</mml:mi><mml:mn>3</mml:mn></mml:msup></mml:math>from Supersymmetric Matrix Quantum Mechanics"}]},{"@id":"https://cir.nii.ac.jp/crid/1360286994320972160","@type":"Article","resourceType":"学術雑誌論文(journal article)","relationType":["isReferencedBy"],"jpcoar:relatedTitle":[{"@value":"Black resonators and geons in AdS\n                    <sub>5</sub>"}]},{"@id":"https://cir.nii.ac.jp/crid/1360306904382678144","@type":"Article","resourceType":"学術雑誌論文(journal article)","relationType":["isReferencedBy"],"jpcoar:relatedTitle":[{"@value":"Lie Algebra and Quantization in Quantum World"}]},{"@id":"https://cir.nii.ac.jp/crid/1360567182398427648","@type":"Article","resourceType":"学術雑誌論文(journal article)","relationType":["isReferencedBy"],"jpcoar:relatedTitle":[{"@value":"Equivalence of large-N gauge theories on a group manifold and its coset space"}]},{"@id":"https://cir.nii.ac.jp/crid/1360861705592211072","@type":"Article","resourceType":"学術雑誌論文(journal article)","relationType":["isReferencedBy"],"jpcoar:relatedTitle":[{"@value":"Category of quantizations and inverse problem"}]},{"@id":"https://cir.nii.ac.jp/crid/2051151842043898496","@type":"Article","resourceType":"学術雑誌論文(journal article)","relationType":["isReferencedBy"],"jpcoar:relatedTitle":[{"@value":"The origin of space-time as seen from matrix model simulations"}]}],"dataSourceIdentifier":[{"@type":"CROSSREF","@value":"10.1103/physrevd.77.126015"},{"@type":"OPENAIRE","@value":"doi_dedup___::23fea3d60fec4ae789de99d981660434"},{"@type":"CROSSREF","@value":"10.1103/physrevd.85.106003_references_DOI_3BMqkps8J1jqg8NlzBqYvE9D5YB"},{"@type":"CROSSREF","@value":"10.1103/physrevlett.102.111601_references_DOI_3BMqkps8J1jqg8NlzBqYvE9D5YB"},{"@type":"CROSSREF","@value":"10.1088/1361-6382/ab1d76_references_DOI_3BMqkps8J1jqg8NlzBqYvE9D5YB"},{"@type":"CROSSREF","@value":"10.1007/978-981-97-6453-2_47_references_DOI_3BMqkps8J1jqg8NlzBqYvE9D5YB"},{"@type":"CROSSREF","@value":"10.1093/ptep/pts004_references_DOI_3BMqkps8J1jqg8NlzBqYvE9D5YB"},{"@type":"CROSSREF","@value":"10.1016/j.nuclphysb.2023.116146_references_DOI_3BMqkps8J1jqg8NlzBqYvE9D5YB"},{"@type":"CROSSREF","@value":"10.1016/j.physletb.2018.05.065_references_DOI_3BMqkps8J1jqg8NlzBqYvE9D5YB"}]}