Open AccessThe Ricci curvature of half-flat manifolds
Author(s) -
Tibra Ali,
Gerald Cleaver
Publication year - 2007
Publication title -
journal of high energy physics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.998
H-Index - 261
eISSN - 1126-6708
pISSN - 1029-8479
DOI - 10.1088/1126-6708/2007/05/009
Subject(s) - holonomy , scalar curvature , riemann curvature tensor , pure mathematics , moduli space , torsion (gastropod) , ricci flat manifold , ricci curvature , mathematics , curvature of riemannian manifolds , curvature , hyperkähler manifold , mathematical analysis , nilpotent , sectional curvature , geometry , medicine , surgery
We derive expressions for the Ricci curvature tensor and scalar in terms ofintrinsic torsion classes of half-flat manifolds by exploiting the relationshipbetween half-flat manifolds and non-compact $G_2$ holonomy manifolds. Ourexpressions are tested for Iwasawa and more general nilpotent manifolds. Wealso derive expressions, in the language of Calabi-Yau moduli spaces, for thetorsion classes and the Ricci curvature of the \emph{particular} half-flatmanifolds that arise naturally via mirror symmetry in flux compactifications.Using these expressions we then derive a constraint on the K\"ahler modulispace of type II string theories on these half-flat manifolds.Comment: 38 pages, no figures. v3: typos corrected, references added, a new appendix added. Version to appear in JHE
Accelerating Research
Robert Robinson Avenue,
Oxford Science Park, Oxford
OX4 4GP, United Kingdom
Address
John Eccles HouseRobert Robinson Avenue,
Oxford Science Park, Oxford
OX4 4GP, United Kingdom