An index for gauge-invariant operators and the Dixmier-Douady invariant

An index for gauge-invariant operators and the Dixmier-Douady invariant

Let G → B be a bundle of compact Lie groups acting on a fiber bundle Y → B. In this paper we introduce and study gauge-equivariant K-theory groups K G(Y ). These groups satisfy the usual properties of the equivariant K-theory groups, but also some new phenomena arise due to the topological non-triviality of the bundle G → B. As an application, we define a gauge-equivariant index for a family of...

Equivariant Dixmier-Douady Classes

An equivariant bundle gerbe à la Meinrenken over a G-manifold M is known to be a special type of S-gerbe over the differentiable stack [M/G]. We prove that the natural morphism relating the Cartan and simplicial models of equivariant cohomology in degree 3 maps the Dixmier-Douady class of an equivariant bundle gerbe à la Meinrenken to the Behrend-Xu-Dixmier-Douady class of the corresponding S-g...

2 Covariance of Gauge Invariant Operators Un -

The cohomology of the BRS operator corresponding to a group of rigid symmetries is studied in a space of local field functionals subjected to a condition of gauge invariance. We propose a procedure based on a filtration operator counting the degree in the infinitesimal parameters of the rigid symmetry transformations. An application to Witten’s topological Yang-Mills theory is given. PACS codes...

Principal Bundles and the Dixmier Douady Class

A systematic consideration of the problem of the reduction and extension of the structure group of a principal bundle is made and a variety of techniques in each case are explored and related to one another. We apply these to the study of the DixmierDouady class in various contexts including string structures, Ures bundles and other examples motivated by considerations from quantum field theory.

The equivariant Chern character and index of G-invariant Operators