Local geometry of the G2 moduli space
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We consider deformations of torsion-free G2 structures, defined by the G2-invariant 3-form $ϕ$ and compute the expansion of the Hodge star of $ϕ$ to fourth order in the deformations of $ϕ$. 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 $ϕ$ we work out the full curvature of this metric and relate it to the Yukawa coupling.
27 pages
27 pages