Classically, a spin structure on the loop space of a manifold is a lift of
the structure group of the looped frame bundle from the loop group to its
universal central extension. Heuristically, the loop space of a manifold is
spin if and only if the manifold itself is a string manifold, against which it
is well-known that only the if-part is true in general. In this article we
develop a new version of spin structures on loop spaces that exists if and only
if the manifold is string, as desired. This new version consists of a classical
spin structure plus a certain fusion product related to loops of frames in the
manifold. We use the lifting gerbe theory of Carey-Murray, recent results of
Stolz-Teichner on loop spaces, and some own results about string geometry and
Brylinski-McLaughlin transgression.Comment: 30 pages. v2 comes with some minor corrections and improvement
