{"@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/1362262943335172736.json","@type":"Article","productIdentifier":[{"identifier":{"@type":"DOI","@value":"10.1142/s0129055x17500155"}},{"identifier":{"@type":"URI","@value":"https://www.worldscientific.com/doi/pdf/10.1142/S0129055X17500155"}}],"dc:title":[{"@value":"Topological field theories on manifolds with Wu structures"}],"description":[{"type":"abstract","notation":[{"@value":"<jats:p>We construct invertible field theories generalizing abelian prequantum spin Chern–Simons theory to manifolds of dimension [Formula: see text] endowed with a Wu structure of degree [Formula: see text]. After analyzing the anomalies of a certain discrete symmetry, we gauge it, producing topological field theories whose path integral reduces to a finite sum, akin to Dijkgraaf–Witten theories. We take a general point of view where the Chern–Simons gauge group and its couplings are encoded in a local system of integral lattices.</jats:p><jats:p>The Lagrangian of these theories has to be interpreted as a class in a generalized cohomology theory in order to obtain a gauge invariant action. We develop a computationally friendly cochain model for this generalized cohomology and use it in a detailed study of the properties of the Wu Chern–Simons action. In the 3-dimensional spin case, the latter provides a definition of the “fermionic correction” introduced recently in the literature on fermionic symmetry protected topological phases.</jats:p><jats:p>In order to construct the state space of the gauged theories, we develop an analogue of geometric quantization for finite abelian groups endowed with a skew-symmetric pairing.</jats:p><jats:p>The physical motivation for this work comes from the fact that in the [Formula: see text] case, the gauged 7-dimensional topological field theories constructed here are essentially the anomaly field theories of the 6-dimensional conformal field theories with [Formula: see text] supersymmetry, as will be discussed elsewhere.</jats:p>"}]}],"creator":[{"@id":"https://cir.nii.ac.jp/crid/1382262943335172736","@type":"Researcher","foaf:name":[{"@value":"Samuel Monnier"}],"jpcoar:affiliationName":[{"@value":"Section de Mathématiques, Université de Genève, 2-4 rue du Lièvre, 1211 Genève 4, Switzerland"}]}],"publication":{"publicationIdentifier":[{"@type":"PISSN","@value":"0129055X"},{"@type":"EISSN","@value":"17936659"}],"prism:publicationName":[{"@value":"Reviews in Mathematical Physics"}],"dc:publisher":[{"@value":"World Scientific Pub Co Pte Ltd"}],"prism:publicationDate":"2017-04-12","prism:volume":"29","prism:number":"05","prism:startingPage":"1750015"},"reviewed":"false","url":[{"@id":"https://www.worldscientific.com/doi/pdf/10.1142/S0129055X17500155"}],"createdAt":"2017-04-13","modifiedAt":"2024-06-23","relatedProduct":[{"@id":"https://cir.nii.ac.jp/crid/1360579813373383040","@type":"Article","resourceType":"学術雑誌論文(journal article)","relationType":["isReferencedBy"],"jpcoar:relatedTitle":[{"@value":"Anomaly Inflow and p-Form Gauge Theories"}]},{"@id":"https://cir.nii.ac.jp/crid/1360580230578992896","@type":"Article","resourceType":"学術雑誌論文(journal article)","relationType":["isReferencedBy"],"jpcoar:relatedTitle":[{"@value":"Global anomalies in 8d supergravity"}]},{"@id":"https://cir.nii.ac.jp/crid/1361694369869089152","@type":"Article","resourceType":"学術雑誌論文(journal article)","relationType":["isReferencedBy"],"jpcoar:relatedTitle":[{"@value":"Anomaly of the Electromagnetic Duality of Maxwell Theory"}]},{"@id":"https://cir.nii.ac.jp/crid/2051433317034804992","@type":"Article","resourceType":"学術雑誌論文(journal article)","relationType":["isReferencedBy"],"jpcoar:relatedTitle":[{"@value":"Some comments on 6D global gauge anomalies"}]}],"dataSourceIdentifier":[{"@type":"CROSSREF","@value":"10.1142/s0129055x17500155"},{"@type":"CROSSREF","@value":"10.1093/ptep/ptab015_references_DOI_H2YGMwmWBvujCnSWIhG7KICG0P4"},{"@type":"CROSSREF","@value":"10.1007/s00220-022-04333-w_references_DOI_H2YGMwmWBvujCnSWIhG7KICG0P4"},{"@type":"CROSSREF","@value":"10.1007/jhep07(2022)125_references_DOI_H2YGMwmWBvujCnSWIhG7KICG0P4"},{"@type":"CROSSREF","@value":"10.1103/physrevlett.123.161601_references_DOI_H2YGMwmWBvujCnSWIhG7KICG0P4"}]}