Duality symmetry and the form fields of M-theory

TL;DR

This paper extends the mathematical framework of M-theory by incorporating dual fields into the topological character formalism, suggesting a unified approach that may involve twisted cohomology theories with higher-degree twists.

Contribution

It introduces an extension of the topological characters to include dual fields, providing a unified treatment of M-theory's four-form and its dual, and explores the potential of twisted cohomology with higher-degree twists.

Findings

Unified treatment of four-form and dual fields in M-theory.

Proposal of a twisted cohomology theory with higher-degree twists.

Insights into the topological structure of M-theory fields.

Abstract

In previous work we derived the topological terms in the M-theory action in terms of certain characters that we defined. In this paper, we propose the extention of these characters to include the dual fields. The unified treatment of the M-theory four-form field strength and its dual leads to several observations. In particular we elaborate on the possibility of a twisted cohomology theory with a twist given by degrees greater than three.