The Clifford Algebra Bundle on Loop Space

Abstract

We construct a Clifford algebra bundle formed from the tangent bundle of the smooth loop space of a Riemannian manifold, which is a bundle of super von Neumann algebras on the loop space. We show that this bundle is in general non-trivial, more precisely that its triviality is obstructed by the transgressions of the second Stiefel-Whitney class and the first (fractional) Pontrjagin class of the manifold.

References in corpus (4)

• A bundle gerbe construction of a spinor bundle from the smooth free loop of a vector bundle
• The spinor bundle on loop space
• 2-vector bundles
• Connes fusion of spinors on loop space