String connections and Chern-Simons theory

Abstract

We present a finite-dimensional and smooth formulation of string structures on spin bundles. It uses trivializations of the Chern-Simons 2-gerbe associated to this bundle. Our formulation is particularly suitable to deal with string connections: it enables us to prove that every string structure admits a string connection and that the possible choices form an affine space. Further we discover a new relation between string connections, 3-forms on the base manifold, and degree three differential cohomology. We also discuss in detail the relation between our formulation of string connections and the original version of Stolz and Teichner.