Rational sphere valued supercocycles in M-theory and type IIA string theory

Abstract

We show that supercocycles on super $L_\infty$-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 $\leftrightarrow$ F1/Dp/NS5 correspondence via dimensional reduction of sphere-valued super-$L_\infty$-cocycles.

19 pages; v2 has some prefactors fixed, role of the rational free loop space made more explicit, exposition improved, v3 is the published version, has background material added on a) parameterized spectra, b) rational homotopy theory and c) spinors