Twisted differential String and Fivebrane structures

TL;DR

This paper reinterprets the Green-Schwarz anomaly cancellation mechanism in heterotic string theory using differential twisted String- and Fivebrane-structures, extending cohomology theories to encode higher gauge anomalies.

Contribution

It introduces a novel framework using differential twisted nonabelian cohomology to describe anomaly cancellation in string theory via higher geometric structures.

Findings

Cocycles define differential twisted String- and Fivebrane-structures.

Green-Schwarz mechanism expressed through nonabelian cohomology.

Differential Bianchi identities captured by L-infinity algebra data.

Abstract

In the background effective field theory of heterotic string theory, the Green-Schwarz anomaly cancellation mechanism plays a key role. Here we reinterpret it and its magnetic dual version in terms of differential twisted String- and differential twisted Fivebrane-structures that generalize the notion of Spin-structures and Spin-lifting gerbes and their differential refinement to smooth Spin-connections. We show that all these structures can be encoded in terms of nonabelian cohomology, twisted nonabelian cohomology, and differential twisted nonabelian cohomology, extending the differential generalized abelian cohomology as developed by Hopkins and Singer and shown by Freed to formalize the global description of anomaly cancellation problems in higher gauge theories arising in string theory. We demonstrate that the Green-Schwarz mechanism for the H_3-field, as well as its magnetic dual version for the H_7-field define cocycles in differential twisted nonabelian cohomology that may be called, respectively, differential twisted Spin(n)-, String(n)- and Fivebrane(n)-structures on target space, where the twist in each case is provided by the obstruction to lifting the classifying map of the gauge bundle through a higher connected cover of U(n) or O(n). We show that the twisted Bianchi identities in string theory can be captured by the (nonabelian) L-infinity-algebra valued differential form data provided by the differential refinements of these twisted cocycles.