M8-H Duality Reduces to Local G2 Invariance

Abstract

The idea of M⁸-H duality has progressed through frustratingly many twists and turns and I have discussed several variants of M⁸-H duality. There are 2 options, call them T and N: either the local tangent space T or normal space N of Y⁴ ⊂ M⁸ is quaternionic and contains a complex subspace C. This makes it possible to map N of Y⁴ ⊂ M⁸ to the space-time X⁴ ⊂ M⁴ x CP₂. Which of them or possibly both? Any integrable distribution of quaternionic normal spaces N is allowed whereas for tangent spaces this is not the case. This led to a too hasty rejection of the T option. The second problem relates to the lack of the concrete realization of the M⁸-H duality.