  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.
