Smooth Fock bundles, and spinor bundles on loop space

Abstract

We address the construction of smooth bundles of fermionic Fock spaces, a problem that appears frequently in fermionic gauge theories. Our main motivation is the spinor bundle on the free loop space of a string manifold, a structure anticipated by Killingback and Stolz–Teichner. We develop a general framework for constructing smooth Fock bundles, and obtain as an application a complete and well-founded construction of smooth spinor bundles on loop space. We also develop a projective version using bundle gerbes and twisted bundles, appropriate for the situation that the base manifold is not string.