Non-Kaehler attracting manifolds

We observe that the new attractor mechanism describing IIB flux vacua for Calabi-Yau compactifications has a possible extension to the landscape of non-Kaehler vacua that emerge in heterotic compactifications with fluxes. We focus on the effective theories coming from compactifications on generalized half-flat manifolds, showing that the Minkowski "attractor points'' for 3-form fluxes are special-hermitian manifolds.Comment: 18 pages. v2: Minor polishing, reference added. v3: More cleanup, final version for JHE

Twisted tori and fluxes: a no go theorem for Lie groups of weak G_2 holonomy

In this paper we prove the theorem that there exists no 7--dimensional Lie group manifold G of weak G2 holonomy. We actually prove a stronger statement, namely that there exists no 7--dimensional Lie group with negative definite Ricci tensor Ric_{IJ}. This result rules out (supersymmetric and non--supersymmetric) Freund--Rubin solutions of M--theory of the form AdS_4\times G and compactifications with non--trivial 4--form fluxes of Englert type on an internal group manifold G. A particular class of such backgrounds which, by our arguments are excluded as bulk supergravity compactifications corresponds to the so called compactifications on twisted--tori, for which G has structure constants $\tau^K{}_{IJ}$ with vanishing trace $\tau^J{}_{IJ}=0$. On the other hand our result does not have bearing on warped compactifications of M--theory to four dimensions and/or to compactifications in the presence of localized sources (D--branes, orientifold planes and so forth). Henceforth our result singles out the latter compactifications as the preferred hunting grounds that need to be more systematically explored in relation with all compactification features involving twisted tori.Comment: 38 pages, tar file containing LaTeX source and youngtab.st

Type II compactifications on manifolds with SU(2) x SU(2) structure

We study compactifications of type II theories on SU(2) x SU(2) structure manifolds to six, five and four spacetime dimensions. We use the framework of generalized geometry to describe the NS-NS sector of such compactifications and derive the structure of their moduli spaces. We show that in contrast to SU(3) x SU(3) structure compactifications, there is no dynamical SU(2) x SU(2) structure interpolating between an SU(2) structure and an identity structure. Furthermore, we formulate type II compactifications on SU(2) x SU(2) structures in the context of exceptional generalized geometry which makes the U-duality group manifest and naturally incorporates the scalar degrees of freedom arising in the Ramond-Ramond sector. Via this formalism we derive the structure of the moduli spaces as it is expected from N=4 supergravity.Comment: 69 pages, v2 published versio

Notes on Heterotic Compactifications

In this technical note we describe a pair of results on heterotic compactifications. First, we give an example demonstrating that the usual statement of the anomaly-freedom constraint for perturbative heterotic compactifications (meaning, matching second Chern characters) is incorrect for compactifications involving torsion-free sheaves. Secondly, we correct errors in the literature regarding the counting of massless particles in heterotic compactifications.Comment: 12 pages, LaTeX, new material on index theory adde