Schreiber Twisted Differential String and Fivebrane Structures

An article we once wrote:

on differential string structures and differential fivebrane structures and their interpretation in terms of the Green-Schwarz mechanism in heterotic string theory. The cohomological theory is part of the story at differential cohomology in a cohesive topos.

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, twisted differential string- andtwisted differential Fivebrane-structures_ that generalize the notion of Spin structure and Spin lifting gerbes and their differential refinement to smooth Spin\mathrm{Spin}-connections. We show that all these structures can be encoded in terms of nonabelian cohomology and twisted nonabelian cohomology and twisted differential 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 3H_3-field, as well as its magnetic dual version for the H 7H_7-field define cocycles in twisted differential nonabelian cohomology that may be called, respectively, differential twisted Spin(n)\mathrm{Spin}(n)-, String(n)\mathrm{String}(n)- and Fivebrane(n)\mathrm{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)U(n) or O(n)O(n). We show that the twisted Bianchi identities in string theory can be captured by the (nonabelian) L-∞ algebra (L-∞ algebroid) valued differential form data provided by the differential refinements of these twisted cocycles.


For a comprehensive list of references see differential cohomology in a cohesive topos – references.

Talk notes about this subject are in

  • Urs Schreiber, Chern-Simons terms on higher moduli stacks, Talk at Hausdorff Institute, Bonn (2011) (pdf)

Last revised on December 17, 2023 at 21:36:29. See the history of this page for a list of all contributions to it.