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.
Keywords
Cite
@article{arxiv.0906.0117,
title = {String Connections and Chern-Simons Theory},
author = {Konrad Waldorf},
journal= {arXiv preprint arXiv:0906.0117},
year = {2013}
}
Comments
55 pages; v2: new section with a better treatment of the relation to string connections of Stolz-Teichner, minor changes otherwise; v3: some newest developments referenced, minor changes; v4 comes with typos corrected and is the final and published version