  We give a construction of the spinor bundle of the loop space of a string
manifold together with its fusion product, inspired by ideas from Stolz and
Teichner. The spinor bundle is a super bimodule bundle for a bundle of Clifford
von Neumann algebras over the free path space, and the fusion product is
defined using Connes fusion of such bimodules. As the main result, we prove
that a spinor bundle with fusion product on a manifold X exists if and only X
admits a string structure.

Differential Geometry;Algebraic Topology;Operator Algebras