{"@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/1360580229822597632.json","@type":"Article","productIdentifier":[{"identifier":{"@type":"DOI","@value":"10.1007/jhep09(2022)022"}},{"identifier":{"@type":"URI","@value":"https://link.springer.com/content/pdf/10.1007/JHEP09(2022)022.pdf"}},{"identifier":{"@type":"URI","@value":"https://link.springer.com/article/10.1007/JHEP09(2022)022/fulltext.html"}},{"identifier":{"@type":"DOI","@value":"10.48550/arxiv.2205.02188"}}],"resourceType":"学術雑誌論文(journal article)","dc:title":[{"@value":"Higher Berry phase of fermions and index theorem"}],"description":[{"type":"abstract","notation":[{"@value":"<jats:title>A<jats:sc>bstract</jats:sc>\n                     </jats:title><jats:p>When a quantum field theory is trivially gapped, its infrared fixed point is an invertible field theory. The partition function of the invertible field theory records the response to various background fields in the long-distance limit. The set of background fields can include spacetime-dependent coupling constants, in which case we call the corresponding invertible theory a parameterized invertible field theory. We study such parameterized invertible field theories arising from free Dirac fermions with spacetime-dependent mass parameters using the Atiyah-Patodi-Singer index theorem for superconnections. In particular, the response to an infinitesimal modulation of the mass is encoded into a higher analog of the Berry curvature, for which we provide a general formula. When the Berry curvature vanishes, the invertible theory can still be nontrivial if there is a remaining torsional Berry phase, for which we list some computable examples.</jats:p>"}]}],"creator":[{"@id":"https://cir.nii.ac.jp/crid/1380580229822597635","@type":"Researcher","foaf:name":[{"@value":"Yichul Choi"}]},{"@id":"https://cir.nii.ac.jp/crid/1380580229822597634","@type":"Researcher","foaf:name":[{"@value":"Kantaro Ohmori"}]}],"publication":{"publicationIdentifier":[{"@type":"EISSN","@value":"10298479"}],"prism:publicationName":[{"@value":"Journal of High Energy Physics"}],"dc:publisher":[{"@value":"Springer Science and Business Media LLC"}],"prism:publicationDate":"2022-09-02","prism:volume":"2022","prism:number":"9","prism:startingPage":"022"},"reviewed":"false","dcterms:accessRights":"http://purl.org/coar/access_right/c_abf2","dc:rights":["https://creativecommons.org/licenses/by/4.0","https://creativecommons.org/licenses/by/4.0"],"url":[{"@id":"https://link.springer.com/content/pdf/10.1007/JHEP09(2022)022.pdf"},{"@id":"https://link.springer.com/article/10.1007/JHEP09(2022)022/fulltext.html"}],"createdAt":"2022-09-05","modifiedAt":"2022-12-24","foaf:topic":[{"@id":"https://cir.nii.ac.jp/all?q=Global%20Symmetries","dc:title":"Global Symmetries"},{"@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=Strongly%20Correlated%20Electrons%20(cond-mat.str-el)","dc:title":"Strongly Correlated Electrons (cond-mat.str-el)"},{"@id":"https://cir.nii.ac.jp/all?q=FOS:%20Physical%20sciences","dc:title":"FOS: Physical sciences"},{"@id":"https://cir.nii.ac.jp/all?q=Topological%20States%20of%20Matter","dc:title":"Topological States of Matter"},{"@id":"https://cir.nii.ac.jp/all?q=QC770-798","dc:title":"QC770-798"},{"@id":"https://cir.nii.ac.jp/all?q=Condensed%20Matter%20-%20Strongly%20Correlated%20Electrons","dc:title":"Condensed Matter - Strongly Correlated Electrons"},{"@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=Nuclear%20and%20particle%20physics.%20Atomic%20energy.%20Radioactivity","dc:title":"Nuclear and particle physics. Atomic energy. Radioactivity"},{"@id":"https://cir.nii.ac.jp/all?q=Anomalies%20in%20Field%20and%20String%20Theories","dc:title":"Anomalies in Field and String Theories"}],"project":[{"@id":"https://cir.nii.ac.jp/crid/1040010457608382336","@type":"Project","projectIdentifier":[{"@type":"KAKEN","@value":"22K13969"},{"@type":"JGN","@value":"JP22K13969"},{"@type":"URI","@value":"https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-22K13969/"}],"notation":[{"@language":"ja","@value":"トポロジカル相のギャップ付き境界条件の分類"},{"@language":"en","@value":"Classificatoin of gapped boundary conditions of topological phases"}]}],"relatedProduct":[{"@id":"https://cir.nii.ac.jp/crid/1050282810828595968","@type":"Article","resourceType":"学術雑誌論文(journal article)","relationType":["references"],"jpcoar:relatedTitle":[{"@language":"en","@value":"Vacuum structure of bifundamental gauge theories at finite topological angles"}]},{"@id":"https://cir.nii.ac.jp/crid/1050855656184504832","@type":"Article","resourceType":"学術雑誌論文(journal article)","relationType":["references"],"jpcoar:relatedTitle":[{"@language":"en","@value":"Center vortex and confinement in Yang–Mills theory and QCD with anomaly-preserving compactifications"}]},{"@id":"https://cir.nii.ac.jp/crid/1050857669062672128","@type":"Article","resourceType":"学術雑誌論文(journal article)","relationType":["references"],"jpcoar:relatedTitle":[{"@language":"en","@value":"Anomaly and superconnection"}]},{"@id":"https://cir.nii.ac.jp/crid/1360011146142961024","@type":"Article","relationType":["references"],"jpcoar:relatedTitle":[{"@value":"Theta, time reversal and temperature"}]},{"@id":"https://cir.nii.ac.jp/crid/1360013171616450304","@type":"Article","relationType":["references"],"jpcoar:relatedTitle":[{"@value":"Symmetry protected topological phases and generalized cohomology"}]},{"@id":"https://cir.nii.ac.jp/crid/1360013172749127040","@type":"Article","relationType":["references"],"jpcoar:relatedTitle":[{"@value":"Superconnections and index theory"}]},{"@id":"https://cir.nii.ac.jp/crid/1360013173138690304","@type":"Article","relationType":["references"],"jpcoar:relatedTitle":[{"@value":"On superconnections and the tachyon effective action"}]},{"@id":"https://cir.nii.ac.jp/crid/1360285710000464256","@type":"Article","resourceType":"学術雑誌論文(journal article)","relationType":["references"],"jpcoar:relatedTitle":[{"@value":"Atiyah-Patodi-Singer index from the domain-wall fermion Dirac operator"}]},{"@id":"https://cir.nii.ac.jp/crid/1360286990770821248","@type":"Article","resourceType":"学術雑誌論文(journal article)","relationType":["references"],"jpcoar:relatedTitle":[{"@value":"On the Cobordism Classification of Symmetry Protected Topological Phases"}]},{"@id":"https://cir.nii.ac.jp/crid/1360292621580890752","@type":"Article","relationType":["references"],"jpcoar:relatedTitle":[{"@value":"Generalized global symmetries"}]},{"@id":"https://cir.nii.ac.jp/crid/1360294643736792832","@type":"Article","resourceType":"学術雑誌論文(journal article)","relationType":["references"],"jpcoar:relatedTitle":[{"@value":"Comments on the Atiyah-Patodi-Singer index theorem, domain wall, and Berry phase"}]},{"@id":"https://cir.nii.ac.jp/crid/1360294643792593536","@type":"Article","resourceType":"学術雑誌論文(journal article)","relationType":["references"],"jpcoar:relatedTitle":[{"@value":"Effective field theories of topological crystalline insulators and topological crystals"}]},{"@id":"https://cir.nii.ac.jp/crid/1360294645353740544","@type":"Article","relationType":["references"],"jpcoar:relatedTitle":[{"@value":"Reflection positivity and invertible topological phases"}]},{"@id":"https://cir.nii.ac.jp/crid/1360294647236618112","@type":"Article","relationType":["references"],"jpcoar:relatedTitle":[{"@value":"Berry phase in quantum field theory: Diabolical points and boundary phenomena"}]},{"@id":"https://cir.nii.ac.jp/crid/1360298760979931648","@type":"Article","relationType":["references"],"jpcoar:relatedTitle":[{"@value":"The fermionic universal one-loop effective action"}]},{"@id":"https://cir.nii.ac.jp/crid/1360298763131737856","@type":"Article","relationType":["references"],"jpcoar:relatedTitle":[{"@value":"Axion effective action"}]},{"@id":"https://cir.nii.ac.jp/crid/1360298763131740032","@type":"Article","relationType":["references"],"jpcoar:relatedTitle":[{"@value":"Global aspects of spaces of vacua"}]},{"@id":"https://cir.nii.ac.jp/crid/1360298763131741184","@type":"Article","relationType":["references"],"jpcoar:relatedTitle":[{"@value":"Strongly coupled QFT dynamics via TQFT coupling"}]},{"@id":"https://cir.nii.ac.jp/crid/1360298763133007616","@type":"Article","relationType":["references"],"jpcoar:relatedTitle":[{"@value":"Adiabatic paths of Hamiltonians, symmetries of topological order, and automorphism codes"}]},{"@id":"https://cir.nii.ac.jp/crid/1360298764518854016","@type":"Article","relationType":["references"],"jpcoar:relatedTitle":[{"@value":"Interface junctions in QCD${}_4$"}]},{"@id":"https://cir.nii.ac.jp/crid/1360574093985914240","@type":"Article","relationType":["references"],"jpcoar:relatedTitle":[{"@value":"Quantal phase factors accompanying adiabatic changes"}]},{"@id":"https://cir.nii.ac.jp/crid/1360576118673062400","@type":"Article","resourceType":"学術雑誌論文(journal article)","relationType":["references"],"jpcoar:relatedTitle":[{"@value":"A physicist-friendly reformulation of the Atiyah-Patodi-Singer index and its mathematical justification"}]},{"@id":"https://cir.nii.ac.jp/crid/1360580230579016192","@type":"Article","resourceType":"学術雑誌論文(journal article)","relationType":["isReferencedBy"],"jpcoar:relatedTitle":[{"@value":"Heterotic global anomalies and torsion Witten index"}]},{"@id":"https://cir.nii.ac.jp/crid/1360580237019909376","@type":"Article","relationType":["references"],"jpcoar:relatedTitle":[{"@value":"Integrating out new fermions at one loop"}]},{"@id":"https://cir.nii.ac.jp/crid/1360584340722529664","@type":"Article","resourceType":"学術雑誌論文(journal article)","relationType":["isReferencedBy"],"jpcoar:relatedTitle":[{"@value":"Higher structures in matrix product states"}]},{"@id":"https://cir.nii.ac.jp/crid/1360853567562141312","@type":"Article","resourceType":"学術雑誌論文(journal article)","relationType":["references"],"jpcoar:relatedTitle":[{"@value":"Topological aspects of 4D Abelian lattice gauge theories with the θ parameter"}]},{"@id":"https://cir.nii.ac.jp/crid/1360855569103820416","@type":"Article","relationType":["references"],"jpcoar:relatedTitle":[{"@value":"Brane-antibrane action from boundary string field theory"}]},{"@id":"https://cir.nii.ac.jp/crid/1360855569598036992","@type":"Article","relationType":["references"],"jpcoar:relatedTitle":[{"@value":"The bi-fundamental gauge theory in 3+1 dimensions: the vacuum structure and a cascade"}]},{"@id":"https://cir.nii.ac.jp/crid/1360855569892026368","@type":"Article","relationType":["references"],"jpcoar:relatedTitle":[{"@value":"Periodic table for topological insulators and superconductors"}]},{"@id":"https://cir.nii.ac.jp/crid/1360857593669265664","@type":"Article","resourceType":"学術雑誌論文(journal article)","relationType":["references"],"jpcoar:relatedTitle":[{"@value":"Matching higher symmetries across Intriligator-Seiberg duality"}]},{"@id":"https://cir.nii.ac.jp/crid/1360861709552393472","@type":"Article","relationType":["references"],"jpcoar:relatedTitle":[{"@value":"Higher-dimensional generalizations of Berry curvature"}]},{"@id":"https://cir.nii.ac.jp/crid/1360869855555618304","@type":"Article","resourceType":"学術雑誌論文(journal article)","relationType":["isReferencedBy"],"jpcoar:relatedTitle":[{"@value":"Constraints on the topology of Type IIB string theory"}]},{"@id":"https://cir.nii.ac.jp/crid/1361137045451535360","@type":"Article","relationType":["references"],"jpcoar:relatedTitle":[{"@value":"Spectral asymmetry and Riemannian geometry. III"}]},{"@id":"https://cir.nii.ac.jp/crid/1361412894851965824","@type":"Article","resourceType":"学術雑誌論文(journal article)","relationType":["references"],"jpcoar:relatedTitle":[{"@value":"Topological order in the color-flavor locked phase of a (\n<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\"><mml:mrow><mml:mn>3</mml:mn><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:math>\n)-dimensional \n<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\"><mml:mi>U</mml:mi><mml:mo mathvariant=\"bold\" stretchy=\"false\">(</mml:mo><mml:mi>N</mml:mi><mml:mo mathvariant=\"bold\" stretchy=\"false\">)</mml:mo></mml:math>\n gauge-Higgs system"}]},{"@id":"https://cir.nii.ac.jp/crid/1361418519808897664","@type":"Article","relationType":["references"],"jpcoar:relatedTitle":[{"@value":"Path-Integral Measure for Gauge-Invariant Fermion Theories"}]},{"@id":"https://cir.nii.ac.jp/crid/1361699994921392768","@type":"Article","relationType":["references"],"jpcoar:relatedTitle":[{"@value":"Topological defects and gapless modes in insulators and superconductors"}]},{"@id":"https://cir.nii.ac.jp/crid/1361699995557955712","@type":"Article","relationType":["references"],"jpcoar:relatedTitle":[{"@value":"Evaluation of the chiral anomaly in gauge theories with<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\"><mml:mrow><mml:msub><mml:mrow><mml:mi>γ</mml:mi></mml:mrow><mml:mrow><mml:mn>5</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math>couplings"}]},{"@id":"https://cir.nii.ac.jp/crid/1361699995950187520","@type":"Article","relationType":["references"],"jpcoar:relatedTitle":[{"@value":"Spectral asymmetry and Riemannian Geometry. I"}]},{"@id":"https://cir.nii.ac.jp/crid/1361981470946468608","@type":"Article","relationType":["references"],"jpcoar:relatedTitle":[{"@value":"Superconnections and the Chern character"}]},{"@id":"https://cir.nii.ac.jp/crid/1362262944631307008","@type":"Article","relationType":["references"],"jpcoar:relatedTitle":[{"@value":"Topological insulators and superconductors: tenfold way and dimensional hierarchy"}]},{"@id":"https://cir.nii.ac.jp/crid/1362262945531413120","@type":"Article","relationType":["references"],"jpcoar:relatedTitle":[{"@value":"The Sum Over Topological Sectors and θ in the 2+1-Dimensional $${\\mathbb{CP}^1 \\sigma}$$-Model"}]},{"@id":"https://cir.nii.ac.jp/crid/1362825893403699584","@type":"Article","relationType":["references"],"jpcoar:relatedTitle":[{"@value":"Boundary string field theory of the<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\"><mml:mi>D</mml:mi><mml:mrow><mml:mrow><mml:mover><mml:mrow><mml:mi>D</mml:mi></mml:mrow><mml:mrow><mml:mi>¯</mml:mi></mml:mrow></mml:mover></mml:mrow></mml:mrow></mml:math>system"}]},{"@id":"https://cir.nii.ac.jp/crid/1362825893578239744","@type":"Article","relationType":["references"],"jpcoar:relatedTitle":[{"@value":"Theta-terms in nonlinear sigma-models"}]},{"@id":"https://cir.nii.ac.jp/crid/1362825895056453504","@type":"Article","relationType":["references"],"jpcoar:relatedTitle":[{"@value":"Universality between vector-like and chiral quiver gauge theories: anomalies and domain walls"}]},{"@id":"https://cir.nii.ac.jp/crid/1362825895497143680","@type":"Article","relationType":["references"],"jpcoar:relatedTitle":[{"@value":"Spectral asymmetry and Riemannian geometry. II"}]},{"@id":"https://cir.nii.ac.jp/crid/1362825895671584384","@type":"Article","relationType":["references"],"jpcoar:relatedTitle":[{"@value":"Comments on abelian Higgs models and persistent order"}]},{"@id":"https://cir.nii.ac.jp/crid/1362825895836489600","@type":"Article","relationType":["references"],"jpcoar:relatedTitle":[{"@value":"Anomalies in the space of coupling constants and their dynamical applications I"}]},{"@id":"https://cir.nii.ac.jp/crid/1363107369840749824","@type":"Article","relationType":["references"],"jpcoar:relatedTitle":[{"@value":"Dai-Freed theorem and topological phases of matter"}]},{"@id":"https://cir.nii.ac.jp/crid/1363388843724892672","@type":"Article","relationType":["references"],"jpcoar:relatedTitle":[{"@value":"A new SU(2) anomaly"}]},{"@id":"https://cir.nii.ac.jp/crid/1363388844588786304","@type":"Article","relationType":["references"],"jpcoar:relatedTitle":[{"@value":"Solitons with fermion number ½"}]},{"@id":"https://cir.nii.ac.jp/crid/1363388846044580352","@type":"Article","relationType":["references"],"jpcoar:relatedTitle":[{"@value":"Fractional Quantum Numbers on Solitons"}]},{"@id":"https://cir.nii.ac.jp/crid/1363670320999990528","@type":"Article","relationType":["references"],"jpcoar:relatedTitle":[{"@value":"Anomalies in the space of coupling constants and their dynamical applications II"}]},{"@id":"https://cir.nii.ac.jp/crid/1363951794154236160","@type":"Article","relationType":["references"],"jpcoar:relatedTitle":[{"@value":"Anomaly and global inconsistency matching: \n<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mi>θ</mml:mi></mml:math>\n angles, \n<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mrow><mml:mi>S</mml:mi><mml:mi>U</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mn>3</mml:mn><mml:mo>)</mml:mo></mml:mrow><mml:mo>/</mml:mo><mml:mi>U</mml:mi><mml:msup><mml:mrow><mml:mo>(</mml:mo><mml:mn>1</mml:mn><mml:mo>)</mml:mo></mml:mrow><mml:mn>2</mml:mn></mml:msup></mml:mrow></mml:math>\n nonlinear sigma model, \n<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mrow><mml:mi>S</mml:mi><mml:mi>U</mml:mi><mml:mo>(</mml:mo><mml:mn>3</mml:mn><mml:mo>)</mml:mo></mml:mrow></mml:math>\n chains, and generalizations"}]},{"@id":"https://cir.nii.ac.jp/crid/1363951794606950528","@type":"Article","relationType":["references"],"jpcoar:relatedTitle":[{"@value":"Ramond-Ramond couplings on brane-antibrane systems"}]},{"@id":"https://cir.nii.ac.jp/crid/1363951795499938176","@type":"Article","relationType":["references"],"jpcoar:relatedTitle":[{"@value":"Anomalies and fermion zero modes on strings and domain walls"}]},{"@id":"https://cir.nii.ac.jp/crid/1363951796265759616","@type":"Article","relationType":["references"],"jpcoar:relatedTitle":[{"@value":"Framed Wilson operators, fermionic strings, and gravitational anomaly in 4d"}]},{"@id":"https://cir.nii.ac.jp/crid/1364233269456689664","@type":"Article","relationType":["references"],"jpcoar:relatedTitle":[{"@value":"Heat Kernels and Dirac Operators"}]},{"@id":"https://cir.nii.ac.jp/crid/2051433317021890560","@type":"Article","resourceType":"学術雑誌論文(journal article)","relationType":["references"],"jpcoar:relatedTitle":[{"@value":"Global inconsistency, 't Hooft anomaly, and level crossing in quantum mechanics"}]},{"@id":"https://cir.nii.ac.jp/crid/2051433317034801664","@type":"Article","resourceType":"学術雑誌論文(journal article)","relationType":["references"],"jpcoar:relatedTitle":[{"@value":"The Atiyah–Patodi–Singer index theorem from the axial anomaly"}]}],"dataSourceIdentifier":[{"@type":"CROSSREF","@value":"10.1007/jhep09(2022)022"},{"@type":"KAKEN","@value":"PRODUCT-24324466"},{"@type":"OPENAIRE","@value":"doi_dedup___::513a9470fa30df714e4383b308c74696"},{"@type":"CROSSREF","@value":"10.1007/jhep10(2022)114_references_DOI_2vheynw810dX06HPAfDsDaENj0v"},{"@type":"CROSSREF","@value":"10.1103/physrevb.109.115152_references_DOI_Lea2C8QWY7VEF4PK4ya4oNShvn2"},{"@type":"CROSSREF","@value":"10.1007/jhep07(2024)112_references_DOI_2vheynw810dX06HPAfDsDaENj0v"}]}