# Twisted Cohomotopy implies M-theory anomaly cancellation on 8-manifolds

## TL;DR

This paper demonstrates that in M-theory on 8-manifolds, the C-field flux quantization within J-twisted Cohomotopy theory ensures anomaly cancellation conditions, linking advanced cohomology to physical consistency.

## Contribution

It establishes a novel connection between non-abelian Cohomotopy theory and M-theory anomaly cancellation on 8-manifolds, providing a new mathematical framework for flux quantization.

## Key findings

- Charge quantization in Cohomotopy implies anomaly cancellation conditions.
- Includes shifted flux quantization and tadpole cancellation.
- Ensures the C-field's integral equation of motion.

## Abstract

We consider the hypothesis that the C-field 4-flux and 7-flux forms in M-theory are in the image of the non-abelian Chern character map from the non-abelian generalized cohomology theory called J-twisted Cohomotopy theory. We prove for M2-brane backgrounds in M-theory on 8-manifolds that such charge quantization of the C-field in Cohomotopy theory implies a list of expected anomaly cancellation conditions, including: shifted C-field flux quantization and C-field tadpole cancellation, but also the DMW anomaly cancellation and the C-field's integral equation of motion.