LAUSR

Abstract We show that supercocycles on super L ∞ -algebras capture, at the rational level, the twisted cohomological charge structure of the fields of M -theory and of type IIA string theory. We show that rational 4-sphere-valued supercocycles for M-branes in M -theory descend to supercocycles in type IIA string theory with coefficients in the free loop space of the 4-sphere, to yield the Ramond–Ramond fields in the rational image of twisted K -theory, with the twist given by the B -field. In particular, we derive the M2/M5 ↔ F1/Dp/NS5 correspondence via dimensional reduction of sphere-valued super- L ∞ -cocycles.