2008/05/31 by Hisham Sati, Urs Schreiber, Jim Stasheff · 1 citation
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Homotopy and Cohomology in Algebraic Topology #Noncommutative and Quantum Gravity Theories #hep-th #math.AT #math.DG
paper · pdf · doi:10.1142/s0129055x09003840
published as Rev.Math.Phys.21:1197-1240,2009 · 34 pages, presentation improved, minor changes
arxiv created 2009/04/09 · openalex publication_date 2009/11/01 · arxiv updated 2010/01/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study the cohomological physics of fivebranes in type II and heterotic string theory. We give an interpretation of the one-loop term in type IIA, which involves the first and second Pontrjagin classes of spacetime, in terms of obstructions to having bundles with certain structure groups. Using a generalization of the Green–Schwarz anomaly cancellation in heterotic string theory which demands the target space to have a String structure, we observe that the "magnetic dual" version of the anomaly cancellation condition can be read as a higher analog of String structure, which we call Fivebrane structure. This involves lifts of orthogonal and unitary structures through higher connected covers which are not just 3- but even 7-connected. We discuss the topological obstructions to the existence of Fivebrane structures. The dual version of the anomaly cancellation points to a relation of string and Fivebrane structures under electric-magnetic duality.