Twistorial cohomotopy implies Green–Schwarz anomaly cancellation

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 Hořava–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 tangentially twisted unstable Cohomotopy theory.

Orbifolds by 2-groups and decomposition

“…(See for example [32] for a mathematical introduction to 2-groups. These structures have a long history in both math and physics, see for example for a few older instances, and [59][60][61][62][63][64][65][66][67][68][69][70][71][72] for some more recent physics descriptions and applications of 2-groups.) When those one-form symmetries act trivially, gauging them results in a global two-form symmetry, hence a decomposition as above, which we will check explicitly.…”