Advances in Theoretical and Mathematical Physics

Volume 13 (2009)

Number 1

Geometric structures on G2 and Spin (7)-manifolds

Pages: 1 – 31

DOI: http://dx.doi.org/10.4310/ATMP.2009.v13.n1.a1

Authors

Jae-Hyouk Lee

Naichung Conan Leung

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.

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