The Rational Higher Structure of M-theory

TL;DR

This paper explores how core structures of string/M-theory can be understood through super homotopy theory, revealing new insights into brane species, dualities, and charge quantization in a rational approximation.

Contribution

It introduces a systematic super homotopy theoretical framework to derive and understand fundamental M-theory structures and dualities in the rational approximation.

Findings

Identifies all super p-brane species and their intersection laws.

Reveals duality relations and black brane configurations.

Recovers twisted K-theory for D-branes and cohomotopy for M-branes.

Abstract

We review how core structures of string/M-theory emerge as higher structures in super homotopy theory; namely from systematic analysis of the brane bouquet of universal invariant higher central extensions growing out of the superpoint. Since super homotopy theory is immensely rich, to start with we consider this in the rational/infinitesimal approximation which ignores torsion-subgroups in brane charges and focuses on tangent spaces of super space-time. Already at this level, super homotopy theory discovers all super $p$-brane species, their intersection laws, their M/IIA-, T- and S-duality relations, their black brane avatars at ADE-singularities, including their instanton contributions, and, last not least, Dirac charge quantization: for the D-branes it recovers twisted K-theory, rationally, but for the M-branes it gives cohomotopy cohomology theory. We close with an outlook on the lift of these results beyond the rational/infinitesimal approximation to a candidate formalization of microscopic M-theory in super homotopy theory.