Geometric structures on G2 and Spin (7)-manifolds

Abstract

This article studies the geometry of moduli spaces of G²-manifolds, associative cycles, coassociative cycles and deformed Donaldson–Thomas bundles. We introduce natural symmetric cubic tensors and differential forms on these moduli spaces. They correspond to Yukawa couplings and correlation functions in M-theory.

We expect that the Yukawa coupling characterizes (co-)associative fibrations on these manifolds. We discuss the Fourier transformation along such fibrations and the analog of the Strominger–Yau–Zaslow mirror conjecture for G²-manifolds.

We also discuss similar structures and transformations for Spin(7)- manifolds.