BUNDLE GERBES APPLIED TO QUANTUM FIELD THEORY

DOI10.1142/S0129055X00000046zbMath0961.81127arXivhep-th/9711133OpenAlexW1968313821MaRDI QIDQ4519831

Michael K. Murray, Jouko Mickelsson, Alan L. Carey

Publication date: 4 December 2000

Published in: Reviews in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/hep-th/9711133

zbMATH Keywords

Riemann surfacesquantum field theoryWZW modelDixmier-Douady classbundle gerbegauge group actionAtiyah-Patodi-Singer index theorybundle of fermionic Fock spacesAPS theoremexistence of string structuresfermions in external fieldsglobal Hamiltonian anomaliesMickelsson-Faddeev cocycle

Mathematics Subject Classification ID

Quantum field theory; related classical field theories (81T99) Moduli problems for topological structures (58D29) Applications of global differential geometry to the sciences (53C80) Applications of PDEs on manifolds (58J90) Other algebro-geometric (co)homologies (e.g., intersection, equivariant, Lawson, Deligne (co)homologies) (14F43) Generalizations of fiber spaces and bundles in algebraic topology (55R65)

Related Items (21)

Bundle gerbes for Chern-Simons and Wess-Zumino-Witten theories ⋮ On the relationship of gerbes to the odd families index theorem ⋮ Topological quantum field theory on non-Abelian gerbes ⋮ Non-associative magnetic translations from parallel transport in projective Hilbert bundles ⋮ Square root of gerbe holonomy and invariants of time-reversal-symmetric topological insulators ⋮ Cyclic cocycles on twisted convolution algebras ⋮ Four-dimensional Wess--Zumino--Witten actions ⋮ The 2-Hilbert space of a prequantum bundle gerbe ⋮ Setting the quantum integrand of M-theory ⋮ A NOTE ON BUNDLE GERBES AND INFINITE-DIMENSIONALITY ⋮ FAMILIES OF DIRAC OPERATORS AND QUANTUM AFFINE GROUPS ⋮ Multiplicative bundle gerbes with connection ⋮ Anomalies and Schwinger terms in NCG field theory models ⋮ WZW BRANES AND GERBES ⋮ Smooth 2-group extensions and symmetries of bundle gerbes ⋮ Courant algebroids ⋮ The Fermi gerbe of Weyl semimetals ⋮ Fusion of symmetric D-branes and Verlinde rings ⋮ Gerbes in geometry, field theory, and quantisation ⋮ Nonabelian bundle gerbes, their differential geometry and gauge theory ⋮ Hamiltonian anomalies from extended field theories

Cites Work

• Chiral anomalies in even and odd dimensions
• Orientation and string structures on loop space
• Hamiltonian interpretation of anomalies
• Holonomy and the Wess-Zumino term
• Principal bundles and the Dixmier Douady class
• Index theory, gerbes, and Hamiltonian quantization
• Faddeev's anomaly and bundle gerbes
• Hilbert space cocycles as representations of \((3+1)\)-D current algebras
• Dirac operators coupled to vector potentials
• THE DE RHAM COMPLEX ON INFINITE DIMENSIONAL MANIFOLDS
• Bundle Gerbes
• Champs continus d'espaces hilbertiens et de $C^*$-algèbres

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