A Note on a Standard Embedding on Half-Flat Manifolds

It is argued that the ten dimensional solution that corresponds to the compactification of $E_8 \times E_8$ heterotic string theory on a half-flat manifold is the product space-time $R^{1,2} \times Z_7$ where $Z_7$ is a generalized cylinder with $G_2$ riemannian holonomy. Standard embedding on $Z_7$ then implies an embedding on the half-flat manifold which involves the torsionful connection rather than the Levi-Civita connection. This leads to the breakdown of $E_8 \times E_8$ to $E_6 \times E_8$, as in the case of the standard embedding on Calabi-Yau manifolds, which agrees with the result derived recently by Gurrieri, Lukas and Micu (arXiv:0709.1932) using a different approach. Green-Schwarz anomaly cancellation is then implemented via the torsionful connection on half-flat manifolds.Comment: 5 pages. v2: 6 pages; slightly reworded; version submitted for publication. v3: uses JHEP3.cls, hence 14 pages now. Essentially same content as before. Article in title changed in accordance with JHEP editor's suggestion. Version to appear in JHE

Power-law Solutions from Heterotic Strings

In this paper, we search for accelerating power-law and ekpyrotic solutions in heterotic string theory with NS-NS fluxes compactified on half-flat and generalized half-flat manifolds. We restrict our searches to the STZ sector of the theory. We also considered linear order $\alpha'$ corrections for the half-flat case. The power-law solutions that we find are neither accelerating nor ekpyrotic in any of the models.Comment: 21 pages. Major revision. Conclusions change

The Ricci Curvature of Half-flat Manifolds

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