Twisted Differential String and Fivebrane Structures

Hisham Sati, Urs Schreiber, Jim Stasheff

Research output: Contribution to journalArticle

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

Original languageEnglish (US)
Pages (from-to)169-213
Number of pages45
JournalCommunications in Mathematical Physics
Volume315
Issue number1
DOIs
StatePublished - Sep 1 2012

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homology
strings
Strings
Non-abelian Cohomology
string theory
String Theory
cancellation
differential algebra
anomalies
Cocycle
Cancellation
Anomaly
classifying
Refinement
bundles
Gerbes
gauge theory
Spin Structure
Effective Field Theory
Differential Forms

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

Cite this

Twisted Differential String and Fivebrane Structures. / Sati, Hisham; Schreiber, Urs; Stasheff, Jim.

In: Communications in Mathematical Physics, Vol. 315, No. 1, 01.09.2012, p. 169-213.

Research output: Contribution to journalArticle

Sati, Hisham ; Schreiber, Urs ; Stasheff, Jim. / Twisted Differential String and Fivebrane Structures. In: Communications in Mathematical Physics. 2012 ; Vol. 315, No. 1. pp. 169-213.
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