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

TL;DR

This paper demonstrates that supercocycles on super $L_$-algebras encode the rational twisted cohomological charges of M-theory and type IIA string theory, revealing new insights into their interrelations and field structures.

Contribution

It introduces sphere-valued supercocycles in super $L_$-algebras that capture the twisted cohomology of M-theory and type IIA string theory at the rational level, including dimensional reduction insights.

Findings

Rational 4-sphere-valued supercocycles describe M-branes in M-theory.

These supercocycles descend to type IIA with coefficients in the free loop space of the 4-sphere.

Derived M2/M5 and F1/Dp/NS5 brane correspondence via dimensional reduction.

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.