## Twisted differential nonabelian cohomology Twisted (n−1)-brane n-bundles and their Chern-Simons (n+1)-bundles with characteristic (n + 2)-classes (2008)

Citations: | 3 - 3 self |

### BibTeX

@MISC{Sati08twisteddifferential,

author = {Hisham Sati and Urs Schreiber and Zoran ˇ Skoda and Danny Stevenson},

title = {Twisted differential nonabelian cohomology Twisted (n−1)-brane n-bundles and their Chern-Simons (n+1)-bundles with characteristic (n + 2)-classes},

year = {2008}

}

### OpenURL

### Abstract

We introduce nonabelian differential cohomology classifying ∞-bundles with smooth connection and their higher gerbes of sections, generalizing [138]. We construct classes of examples of these from lifts, twisted lifts and obstructions to lifts through shifted central extensions of groups by the shifted abelian n-group B n−1 U(1). Notable examples are String 2-bundles [9] and Fivebrane 6-bundles [133]. The obstructions to lifting ordinary principal bundles to these, hence in particular the obstructions to lifting Spin-structures to String-structures [13] and further to Fivebrane-structures [133, 52], are abelian Chern-Simons 3- and 7-bundles with characteristic class the first and second fractional Pontryagin class, whose abelian cocycles have been constructed explicitly by Brylinski and McLaughlin [35, 36]. We realize their construction as an abelian component of obstruction theory in nonabelian cohomology by ∞-Lieintegrating the L∞-algebraic data in [132]. As a result, even if the lift fails, we obtain twisted String 2- and twisted Fivebrane 6-bundles classified in twisted nonabelian (differential) cohomology and generalizing the twisted bundles appearing in twisted K-theory. We explain the Green-Schwarz mechanism in heterotic string theory in terms of twisted String 2-bundles and its magnetic dual version – according to [133] – in terms of twisted Fivebrane 6-bundles. We close by transgressing differential cocycles to mapping