The Ricci Curvature of Half-flat Manifolds

Abstract

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 Kähler moduli space of type II string theories on these half-flat manifolds.

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

References in corpus (5)

• SU(3) x SU(3) compactification and mirror duals of magnetic fluxes
• The Ricci tensor of SU(3)-manifolds
• A mini-course on topological strings
• Towards reduction of type II theories on SU(3) structure manifolds
• Topological strings and their physical applications

Cited by in corpus (12)

• Towards Classical de Sitter Solutions in String Theory
• De Sitter hunting in a classical landscape
• Universal de Sitter solutions at tree-level
• Heterotic String Compactifications on Half-flat Manifolds II
• AdS vacua with scale separation from IIB supergravity
• G-structures and Domain Walls in Heterotic Theories
• Systematics of Type IIA moduli stabilisation
• Lifshitz backgrounds from 10d supergravity
• Half-flat structures on products of three-dimensional Lie groups
• KK-monopoles and G-structures in M-theory/type IIA reductions
• Topological A-Type Models with Flux
• Generalized Compactification in Heterotic String Theory