Local geometry of the G2 moduli space

Abstract

We consider deformations of torsion-free G2 structures, defined by the G2-invariant 3-form $\varphi$ and compute the expansion of the Hodge star of $\varphi$ to fourth order in the deformations of $\varphi$. By considering M-theory compactified on a G2 manifold, the G2 moduli space is naturally complexified, and we get a Kahler metric on it. Using the expansion of the Hodge star of $\varphi$ we work out the full curvature of this metric and relate it to the Yukawa coupling.

27 pages

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Cited by in corpus (16)

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• The infinitesimal moduli space of heterotic $G_2$ systems
• Infinitesimal moduli of G2 holonomy manifolds with instanton bundles
• Moduli spaces of G2 manifolds
• Foliated eight-manifolds for M-theory compactification
• Estimates and monotonicity for a heat flow of isometric G2-structures
• Generalising G${}_{\text{2}}$ geometry: involutivity, moment maps and moduli
• Betti numbers of a class of barely G2 manifolds
• G2-structures for N=1 supersymmetric AdS4 solutions of M-theory
• On the incompleteness of $G_2$-moduli spaces along degenerating families of $G_2$-manifolds
• The Space of Closed $G_2$-Structures. I. Connections
• Conformal transformations of the pseudo-Riemannian metric of a homogeneous pair
• Geometry and periods of $G_2$-moduli spaces