On the topological interpretation of gravitational anomalies
Identifieur interne : 000578 ( Istex/Corpus ); précédent : 000577; suivant : 000579On the topological interpretation of gravitational anomalies
Auteurs : Denis PerrotSource :
- Journal of Geometry and Physics [ 0393-0440 ] ; 2001.
English descriptors
- KwdEn :
- Algebra, Anomaly, Anomaly formula, Associative algebra, Bott periodicity, Characteristic classes, Chern, Chern character, Cochains, Cohomology, Compact support, Conformal, Conformal anomalies, Conformal transformations, Connes, Cyclic, Cyclic cohomology, Diffeomorphisms, Differential algebra, Differential forms, Differential operator, Elsevier science, Equivariant, Equivariant cohomology, Equivariant cohomology class, Equivariant homology, Exterior algebra, Gauge group, Gauge theories, Ghost vector, Gravitational anomalies, Gravitational anomaly, Gravitational case, Homogeneous cochains, Homotopy quotient, Index theorem, Invariant forms, Inverse limit, Loop group, Matrix, Noncommutative geometry, Nontrivial, Nontrivial loops, Operator algebras, Orientationpreserving diffeomorphisms, Particular case, Perrot, Perrot journal, Pontrjagin classes, Pontrjagin ring, Principal bundle, Riemann surface, Riemann surfaces, Right composition, Structure group, Tensor product, Topological, Topological anomaly, Topological anomaly formula, Topological interpretation, Weil algebra.
- Teeft :
- Algebra, Anomaly, Anomaly formula, Associative algebra, Bott periodicity, Characteristic classes, Chern, Chern character, Cochains, Cohomology, Compact support, Conformal, Conformal anomalies, Conformal transformations, Connes, Cyclic, Cyclic cohomology, Diffeomorphisms, Differential algebra, Differential forms, Differential operator, Elsevier science, Equivariant, Equivariant cohomology, Equivariant cohomology class, Equivariant homology, Exterior algebra, Gauge group, Gauge theories, Ghost vector, Gravitational anomalies, Gravitational anomaly, Gravitational case, Homogeneous cochains, Homotopy quotient, Index theorem, Invariant forms, Inverse limit, Loop group, Matrix, Noncommutative geometry, Nontrivial, Nontrivial loops, Operator algebras, Orientationpreserving diffeomorphisms, Particular case, Perrot, Perrot journal, Pontrjagin classes, Pontrjagin ring, Principal bundle, Riemann surface, Riemann surfaces, Right composition, Structure group, Tensor product, Topological, Topological anomaly, Topological anomaly formula, Topological interpretation, Weil algebra.
Abstract
Abstract: We consider the mixed gravitational Yang–Mills anomaly as the coupling between the K-theory and K-homology of a C∗-algebra crossed product. The index theorem of Connes–Moscovici allows to compute the Chern character of the K-cycle by local formulae involving connections and curvatures. It gives a topological interpretation to the anomaly, in the sense of noncommutative algebras.
Url:
DOI: 10.1016/S0393-0440(01)00002-X
Links to Exploration step
ISTEX:1B415082CA2F85BD668B40FD53FD9DA836A39C45Le document en format XML
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quotient</term><term>Index theorem</term><term>Invariant forms</term><term>Inverse limit</term><term>Loop group</term><term>Matrix</term><term>Noncommutative geometry</term><term>Nontrivial</term><term>Nontrivial loops</term><term>Operator algebras</term><term>Orientationpreserving diffeomorphisms</term><term>Particular case</term><term>Perrot</term><term>Perrot journal</term><term>Pontrjagin classes</term><term>Pontrjagin ring</term><term>Principal bundle</term><term>Riemann surface</term><term>Riemann surfaces</term><term>Right composition</term><term>Structure group</term><term>Tensor product</term><term>Topological</term><term>Topological anomaly</term><term>Topological anomaly formula</term><term>Topological interpretation</term><term>Weil algebra</term></keywords></textClass><langUsage><language ident="en">en</language></langUsage></profileDesc></teiHeader><front><div type="abstract" xml:lang="en">Abstract: We consider the mixed gravitational Yang–Mills anomaly as the coupling 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The index theorem of Connes–Moscovici allows to compute the Chern character of the K-cycle by local formulae involving connections and curvatures. 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The index theorem of Connes–Moscovici allows to compute the Chern character of the K-cycle by local formulae involving connections and curvatures. 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The index theorem of Connes–Moscovici allows to compute the Chern character of the K-cycle by local formulae involving connections and curvatures. It gives a topological interpretation to the anomaly, in the sense of noncommutative algebras.</p></abstract><textClass><keywords scheme="keyword"><list><head>MSC</head><item><term>19D55</term></item><item><term>81T13</term></item><item><term>81T50</term></item></list></keywords></textClass><textClass><keywords scheme="keyword"><list><head>Keywords</head><item><term>Quantum field theory</term></item></list></keywords></textClass><textClass><keywords scheme="keyword"><list><head>Keywords</head><item><term>K-theory</term></item><item><term>Cyclic cohomology</term></item><item><term>Gauge theories</term></item></list></keywords></textClass></profileDesc><revisionDesc><change when="2001">Published</change></revisionDesc></teiHeader></istex:fulltextTEI><json:item><extension>txt</extension><original>false</original><mimetype>text/plain</mimetype><uri>https://api.istex.fr/document/1B415082CA2F85BD668B40FD53FD9DA836A39C45/fulltext/txt</uri></json:item></fulltext><metadata><istex:metadataXml wicri:clean="Elsevier, elements deleted: body; tail"><istex:xmlDeclaration>version="1.0" encoding="utf-8"</istex:xmlDeclaration><istex:docType PUBLIC="-//ES//DTD journal article DTD version 4.5.2//EN//XML" URI="art452.dtd" name="istex:docType"></istex:docType><istex:document><converted-article version="4.5.2" docsubtype="fla"><item-info><jid>GEOPHY</jid><aid>700</aid><ce:pii>S0393-0440(01)00002-X</ce:pii><ce:doi>10.1016/S0393-0440(01)00002-X</ce:doi><ce:copyright type="full-transfer" year="2001">Elsevier Science B.V.</ce:copyright></item-info><head><ce:title>On the topological interpretation of gravitational anomalies</ce:title><ce:author-group><ce:author><ce:given-name>Denis</ce:given-name><ce:surname>Perrot</ce:surname><ce:cross-ref refid="FN1"><ce:sup>1</ce:sup></ce:cross-ref><ce:e-address>perrot@cpt.univ-mrs.fr</ce:e-address></ce:author><ce:affiliation><ce:textfn>Centre de Physique Théorique, CNRS-Luminy, Case 907, F-13288 Marseille Cedex 9, France</ce:textfn></ce:affiliation><ce:footnote id="FN1"><ce:label>1</ce:label><ce:note-para>Allocataire de recherche MENRT.</ce:note-para></ce:footnote></ce:author-group><ce:date-received day="14" month="6" year="2000"></ce:date-received><ce:abstract><ce:section-title>Abstract</ce:section-title><ce:abstract-sec><ce:simple-para>We consider the mixed gravitational Yang–Mills anomaly as the coupling between the <ce:italic>K</ce:italic>-theory and <ce:italic>K</ce:italic>-homology of a <math altimg="si1.gif">C<sup>∗</sup></math>-algebra crossed product. The index theorem of Connes–Moscovici allows to compute the Chern character of the <ce:italic>K</ce:italic>-cycle by local formulae involving connections and curvatures. It gives a topological interpretation to the anomaly, in the sense of noncommutative algebras.</ce:simple-para></ce:abstract-sec></ce:abstract><ce:keywords class="msc"><ce:section-title>MSC</ce:section-title><ce:keyword><ce:text>19D55</ce:text></ce:keyword><ce:keyword><ce:text>81T13</ce:text></ce:keyword><ce:keyword><ce:text>81T50</ce:text></ce:keyword></ce:keywords><ce:keywords class="idt"><ce:section-title>Keywords</ce:section-title><ce:keyword><ce:text>Quantum field theory</ce:text></ce:keyword></ce:keywords><ce:keywords class="keyword"><ce:section-title>Keywords</ce:section-title><ce:keyword><ce:text><ce:italic>K</ce:italic>-theory</ce:text></ce:keyword><ce:keyword><ce:text>Cyclic cohomology</ce:text></ce:keyword><ce:keyword><ce:text>Gauge theories</ce:text></ce:keyword></ce:keywords></head></converted-article></istex:document></istex:metadataXml><mods version="3.6"><titleInfo><title>On the topological interpretation of gravitational anomalies</title></titleInfo><titleInfo type="alternative" contentType="CDATA"><title>On the topological interpretation of gravitational anomalies</title></titleInfo><name type="personal"><namePart type="given">Denis</namePart><namePart type="family">Perrot</namePart><affiliation>Centre de Physique Théorique, CNRS-Luminy, Case 907, F-13288 Marseille Cedex 9, France</affiliation><affiliation>E-mail: perrot@cpt.univ-mrs.fr</affiliation><description>Allocataire de recherche MENRT.</description><role><roleTerm type="text">author</roleTerm></role></name><typeOfResource>text</typeOfResource><genre type="research-article" displayLabel="Full-length article" authority="ISTEX" authorityURI="https://content-type.data.istex.fr" valueURI="https://content-type.data.istex.fr/ark:/67375/XTP-1JC4F85T-7">research-article</genre><originInfo><publisher>ELSEVIER</publisher><dateIssued encoding="w3cdtf">2001</dateIssued><copyrightDate encoding="w3cdtf">2001</copyrightDate></originInfo><language><languageTerm type="code" authority="iso639-2b">eng</languageTerm><languageTerm type="code" authority="rfc3066">en</languageTerm></language><abstract lang="en">Abstract: We consider the mixed gravitational Yang–Mills anomaly as the coupling between the K-theory and K-homology of a C∗-algebra crossed product. The index theorem of Connes–Moscovici allows to compute the Chern character of the K-cycle by local formulae involving connections and curvatures. It gives a topological interpretation to the anomaly, in the sense of noncommutative algebras.</abstract><subject><genre>MSC</genre><topic>19D55</topic><topic>81T13</topic><topic>81T50</topic></subject><subject><genre>Keywords</genre><topic>Quantum field theory</topic></subject><subject><genre>Keywords</genre><topic>K-theory</topic><topic>Cyclic cohomology</topic><topic>Gauge theories</topic></subject><relatedItem type="host"><titleInfo><title>Journal of Geometry and Physics</title></titleInfo><titleInfo type="abbreviated"><title>GEOPHY</title></titleInfo><genre type="journal" authority="ISTEX" authorityURI="https://publication-type.data.istex.fr" valueURI="https://publication-type.data.istex.fr/ark:/67375/JMC-0GLKJH51-B">journal</genre><originInfo><publisher>ELSEVIER</publisher><dateIssued encoding="w3cdtf">200107</dateIssued></originInfo><identifier type="ISSN">0393-0440</identifier><identifier type="PII">S0393-0440(00)X0075-7</identifier><part><date>200107</date><detail type="volume"><number>39</number><caption>vol.</caption></detail><detail type="issue"><number>1</number><caption>no.</caption></detail><extent unit="issue-pages"><start>1</start><end>96</end></extent><extent unit="pages"><start>82</start><end>96</end></extent></part></relatedItem><identifier type="istex">1B415082CA2F85BD668B40FD53FD9DA836A39C45</identifier><identifier type="ark">ark:/67375/6H6-Z4WR0FK8-0</identifier><identifier type="DOI">10.1016/S0393-0440(01)00002-X</identifier><identifier type="PII">S0393-0440(01)00002-X</identifier><accessCondition type="use and reproduction" contentType="copyright">©2001 Elsevier Science B.V.</accessCondition><recordInfo><recordContentSource authority="ISTEX" authorityURI="https://loaded-corpus.data.istex.fr" valueURI="https://loaded-corpus.data.istex.fr/ark:/67375/XBH-HKKZVM7B-M">elsevier</recordContentSource><recordOrigin>Elsevier Science B.V., ©2001</recordOrigin></recordInfo></mods><json:item><extension>json</extension><original>false</original><mimetype>application/json</mimetype><uri>https://api.istex.fr/document/1B415082CA2F85BD668B40FD53FD9DA836A39C45/metadata/json</uri></json:item></metadata><serie></serie></istex></record>Pour manipuler ce document sous Unix (Dilib)
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|étape= Corpus
|type= RBID
|clé= ISTEX:1B415082CA2F85BD668B40FD53FD9DA836A39C45
|texte= On the topological interpretation of gravitational anomalies
}}
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