Twisted Differential String and Fivebrane Structures
By H. Sati, Urs Schreiber, J. Stasheff. 2009
147 citations recorded by the source corpus.
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 H3-field, as well as its magnetic dual version for the H7-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.
Subfields: Mathematical Physics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/fdb71ed7276ad460c6f158bfc8b2e78c1193b31b
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In Mathematical Physics
- E. Sharpe
- Urs Schreiber
- Danny Stevenson
- T. Nikolaus
- John C. Baez
- A. Henriques
- John Huerta
- Andreas Gustavsson
In Nuclear and High Energy Physics
In Statistical and Nonlinear Physics
Citations in the corpus
- Principal ∞\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\infty $$\end{document}-bundles: general theory (2012, background): “In recent years it has become clear that various applications, notably in “Stringgeometry” [27,28], involve a notion of principal bundleswhere geometric groupsG are generalized to geometric grouplike A∞-spaces, in other words geometric ∞-groups: geometric objects that are equippedwith a group struct”
- Notes on generalized global symmetries in QFT (2015, background): “[34–36]; see also [37] for a discussion of the Green-Schwarz anomaly in present language.”