The Ricci Curvature of Half-flat Manifolds

Details The Ricci Curvature of Half-flat Manifolds The Ricci Curvature of Half-flat Manifolds

2006-12-16

arxiv.org/abs/hep-th/0612171v3

JHEP 0705:009,2007

Physics

High Energy Physics

High Energy Physics - Theory

38 pages, no figures. v3: typos corrected, references added, a new appendix added. Version to appear in JHEP

Scientific paper

10.1088/1126-6708/2007/05/009

We derive expressions for the Ricci curvature tensor and scalar in terms of intrinsic torsion classes of half-flat manifolds by exploiting the relationship between half-flat manifolds and non-compact $G_2$ holonomy manifolds. Our expressions are tested for Iwasawa and more general nilpotent manifolds. We also derive expressions, in the language of Calabi-Yau moduli spaces, for the torsion classes and the Ricci curvature of the \emph{particular} half-flat manifolds that arise naturally via mirror symmetry in flux compactifications. Using these expressions we then derive a constraint on the K\"ahler moduli space of type II string theories on these half-flat manifolds.

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