Communications in Mathematical Physics

, Volume 315, Issue 1, pp 169–213 | Cite as

Twisted Differential String and Fivebrane Structures

  • Hisham Sati
  • Urs Schreiber
  • Jim Stasheff


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 -algebra valued differential form data provided by the differential refinements of these twisted cocycles.


Heterotic String Anomaly Cancellation Chern Character Gauge Bundle String Structure 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag 2012

Authors and Affiliations

  1. 1.Department of MathematicsYale UniversityNew HavenUSA
  2. 2.Fachbereich MathematikUniversität HamburgHamburgGermany
  3. 3.Department of MathematicsUniversity of PennsylvaniaPhiladelphiaUSA
  4. 4.Department of MathematicsUniversity of MarylandCollege ParkUSA
  5. 5.Department of MathematicsUtrecht UniversityUtrechtThe Netherlands

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