The WZW term of the M5-brane and differential cohomotopy

Abstract

We combine rational homotopy theory and higher Lie theory to describe the WZW term in the M5-brane sigma model. We observe that this term admits a natural interpretation as a twisted 7-cocycle on super-Minkowski spacetime with coefficients in the rational 4-sphere. This exhibits the WZW term as an element in twisted cohomology, with the twist given by the cocycle of the M2-brane. We consider integration of this rational situation to differential cohomology and differential cohomotopy.

12 pages

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