Twistorial Cohomotopy implies Green-Schwarz anomaly cancellation

TL;DR

This paper links advanced mathematical structures in twistorial cohomotopy to the Green-Schwarz anomaly cancellation mechanism, providing a new perspective on M-theory's mathematical foundation and its relation to string theory.

Contribution

It characterizes the cohomology and homotopy types relevant to M-theory, connecting them to the Green-Schwarz anomaly cancellation and proposing a mathematical foundation based on J-twisted Cohomotopy theory.

Findings

Relations in cohomology generators match Green-Schwarz anomaly cancellation conditions.

Mathematical structures align with Horava-Witten's extension of the Green-Schwarz mechanism.

Supports the hypothesis that M-theory's foundation involves charge quantization in Cohomotopy.

Abstract

We characterize the integral cohomology and the rational homotopy type of the maximal Borel-equivariantization of the combined Hopf/twistor fibration, and find that subtle relations satisfied by the cohomology generators are just those that govern Horava-Witten's proposal for the extension of the Green-Schwarz mechanism from heterotic string theory to heterotic M-theory. We discuss how this squares with the Hypothesis H that the elusive mathematical foundation of M-theory is based on charge quantization in J-twisted Cohomotopy theory.