Abstract
We consider deformations of torsion-free G 2 structures, defined by the G 2-invariant 3-form φ and compute the expansion of \({\ast \varphi }\) to fourth order in the deformations of φ. By considering M-theory compactified on a G 2 manifold, the G 2 moduli space is naturally complexified, and we get a Kähler metric on it. Using the expansion of \({\ast \varphi }\), we work out the full curvature of this metric and relate it to the Yukawa coupling.
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Communicated by G.W. Gibbons
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Grigorian, S., Yau, ST. Local Geometry of the G 2 Moduli Space. Commun. Math. Phys. 287, 459–488 (2009). https://doi.org/10.1007/s00220-008-0595-1
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DOI: https://doi.org/10.1007/s00220-008-0595-1