(Weak) G_2 Holonomy from Self-duality, Flux and Supersymmetry

The aim of this paper is two-fold. First, we provide a simple and pedagogical discussion of how compactifications of M-theory or supergravity preserving some four-dimensional supersymmetry naturally lead to reduced holonomy or its generalization, reduced weak holonomy. We relate the existence of a (conformal) Killing spinor to the existence of certain closed and co-closed p-forms, and to the metric being Ricci flat or Einstein. Then, for seven-dimensional manifolds, we show that octonionic self-duality conditions on the spin connection are equivalent to G_2 holonomy and certain generalized self-duality conditions to weak G_2 holonomy. The latter lift to self-duality conditions for cohomogeneity-one spin(7) metrics. To illustrate the power of this approach, we present several examples where the self-duality condition largely simplifies the derivation of a G_2 or weak G_2 metric.Comment: references added, 25 pages, no figures, Late

Five-Brane Thresholds and Membrane Instantons in Four-Dimensional Heterotic M-Theory

The effective four-dimensional supergravity of M-theory compactified on the orbifold S^1/Z_2 and a Calabi-Yau threefold includes in general moduli supermultiplets describing massless modes of five-branes. For each brane, one of these fields corresponds to fluctuations along the interval. The five-brane also leads to modifications of the anomaly-cancelling terms in the eleven-dimensional theory, including gauge contributions located on their world-volumes. We obtain the interactions of the brane "interval modulus" predicted by these five-brane-induced anomaly-cancelling terms and we construct their effective supergravity description. In the condensed phase, these interaction terms generate an effective non-perturbative superpotential which can also be interpreted as instanton effects of open membranes stretching between five-branes and the S^1/Z_2 fixed hyperplanes. Aspects of the vacuum structure of the effective supergravity are also briefly discussed.Comment: 39 pages. Published version. Changes in introduction, appendix and reference

A second look at gauged supergravities from fluxes in M-theory

We investigate reductions of M-theory beyond twisted tori by allowing the presence of KK6 monopoles (KKO6-planes) compatible with N=4 supersymmetry in four dimensions. The presence of KKO6-planes proves crucial to achieve full moduli stabilisation as they generate new universal moduli powers in the scalar potential. The resulting gauged supergravities turn out to be compatible with a weak G2 holonomy at N=1 as well as at some non-supersymmetric AdS4 vacua. The M-theory flux vacua we present here cannot be obtained from ordinary type IIA orientifold reductions including background fluxes, D6-branes (O6-planes) and/or KK5 (KKO5) sources. However, from a four-dimensional point of view, they still admit a description in terms of so-called non-geometric fluxes. In this sense we provide the M-theory interpretation for such non-geometric type IIA flux vacua.Comment: 46 pages. Published version. Minor changes, references adde

Non-unimodular reductions and N = 4 gauged supergravities

We analyze the class of four-dimensional N = 4 supergravities obtained by gauging the axionic shift and axionic rescaling symmetries. These theories are formulated with the machinery of embedding tensors and shown to be deducible from higher dimensions using a Scherk--Schwarz reduction with a twist by a non-compact symmetry. This allows to evade the usual unimodularity requirement and completes the dictionary between heterotic gaugings and fluxes, at least for the "geometric sector".Comment: 15 page

Supergravity and Supersymmetry Breaking in Four and Five Dimensions

We discuss supersymmetry breaking in the field-theoretical limit of the strongly-coupled heterotic string compactified on a Calabi-Yau manifold, from the different perspectives of four and five dimensions. The former applies to light degrees of freedom below the threshold for five-dimensional Kaluza-Klein excitations, whereas the five-dimensional perspective is also valid up to the Calabi-Yau scale. We show how, in the latter case, two gauge sectors separated in the fifth dimension are combined to form a consistent four-dimensional supergravity. In the lowest order of the $\kappa^{2/3}$ expansion, we show how a four-dimensional supergravity with gauge kinetic function $f_{1,2}=S$ is reproduced, and we show how higher-order terms give rise to four-dimensional operators that differ in the two gauge sectors. In the four-dimensional approach, supersymmetry is seen to be broken when condensates form on one or both walls, and the goldstino may have a non-zero dilatino component. As in the five-dimensional approach, the Lagrangian is not a perfect square, and we have not identified a vacuum with broken supersymmetry and zero vacuum energy. We derive soft supersymmetry-breaking terms for non-standard perturbative embeddings, that are relevant in more general situations such as type I/type IIB orientifold models.Comment: 17 pages, Late