Gerbes in Geometry, Field Theory, and Quantisation
نویسندگان
چکیده
منابع مشابه
Bundle Gerbes Applied to Quantum Field Theory
This paper reviews recent work on a new geometric object called a bundle gerbe and discusses some new examples arising in quantum field theory. One application is to an Atiyah-Patodi-Singer index theory construction of the bundle of fermionic Fock spaces parametrized by vector potentials in odd space dimensions and a proof that this leads in a simple manner to the known Schwinger terms (Mickels...
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This thesis reviews the theory of bundle gerbes and then examines the higher dimensional notion of a bundle 2-gerbe. The notion of a bundle 2-gerbe connection and 2-curving are introduced and it is shown that there is a class in H(M ;Z) associated to any bundle 2-gerbe.
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The reduction of the E8 gauge theory to ten dimensions leads to a loop group, which in relation to twisted K-theory has a Dixmier-Douady class identified with the Neveu-Schwarz H-field. We give an interpretation of the degree two part of the etaform by comparing the adiabatic limit of the eta invariant with the one loop term in type IIA. More generally, starting with a G-bundle, the comparison ...
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We discuss certain aspects of the combinatorial approach to the differential geometry of non-abelian gerbes due to W. Messing and the author [5], and give a more direct derivation of the associated cocycle equations. This leads us to a more restrictive definition than in [5] of the corresponding coboundary relations. We also show that the diagrammatic proofs of certain local curving and curvatu...
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The infinitesimal symmetries of a fully decomposed non-Abelian gerbe can be generated in terms of a nilpotent BRST operator, which is here constructed. The appearing fields find a natural interpretation in terms of the universal gerbe, a generalisation of the universal bundle. We comment on the construction of observables in the arising Topological Quantum Field Theory. It is also shown how the...
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ژورنال
عنوان ژورنال: Complex Manifolds
سال: 2021
ISSN: 2300-7443
DOI: 10.1515/coma-2020-0112