Mathematics – Algebraic Topology
Scientific paper
2008-05-05
Rev.Math.Phys.21:1197-1240,2009
Mathematics
Algebraic Topology
34 pages, presentation improved, minor changes
Scientific paper
10.1142/S0129055X09003840
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 cancelation in heterotic string theory which demands the target space to have a String structure, we observe that the "magnetic dual" version of the anomaly cancelation 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 cancelation points to a relation of String and Fivebrane structures under electric-magnetic duality.
Sati Hisham
Schreiber Urs
Stasheff Jim
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