Showing papers on "Superpotential published in 2005"
TL;DR: In this article, it was shown that flux compactifications of type IIA string theory can classically stabilize all geometric moduli, including all moduli stabilized at arbitrarily large volume, weak coupling, and small negative cosmological constant.
Abstract: We demonstrate that flux compactifications of type IIA string theory can classically stabilize all geometric moduli. For a particular orientifold background, we explicitly construct an infinite family of supersymmetric vacua with all moduli stabilized at arbitrarily large volume, weak coupling, and small negative cosmological constant. We obtain these solutions from both ten-dimensional and four-dimensional perspectives. For more general backgrounds, we study the equations for supersymmetric vacua coming from the effective superpotential and show that all geometric moduli can be stabilized by fluxes. We comment on the resulting picture of statistics on the landscape of vacua.
505 citations
TL;DR: The N = 1 effective action for generic type IIA Calabi-Yau orientifolds in the presence of background fluxes is computed from a Kaluza-Klein reduction as discussed by the authors.
391 citations
TL;DR: In this paper, the authors considered = 1 compactifications of the type-IIA theory on the T6/(Z2 × Z2) orbifold and O6 orientifold, in the presence of D6-branes and general NSNSNS, RR and Scherk-Schwarz geometrical fluxes.
Abstract: We consider = 1 compactifications of the type-IIA theory on the T6/(Z2 × Z2) orbifold and O6 orientifold, in the presence of D6-branes and general NSNS, RR and Scherk-Schwarz geometrical fluxes. Introducing a suitable dual formulation of the theory, we derive and solve the Bianchi identities, and show how certain combinations of fluxes can relax the constraints on D6-brane configurations coming from the cancellation of RR tadpoles. We then compute, via generalized dimensional reduction, the = 1, D = 4 effective potential for the seven main moduli, and comment on the relation with truncated = 4 gaugings. As a byproduct, we obtain a general geometrical expression for the superpotential. We finally identify a family of fluxes, compatible with all Bianchi identities, that perturbatively stabilize all seven moduli in supersymmetric AdS4.
295 citations
TL;DR: In this paper, the authors studied the distribution of nonsupersymmetric flux vacua in IIb string theory compactified on Calabi-Yau manifolds, and showed that the basic structure of this problem is that of finding eigenvectors of the matrix of second derivatives of the superpotential.
Abstract: We continue the study of the distribution of nonsupersymmetric flux vacua in IIb string theory compactified on Calabi-Yau manifolds, as in hep-th/0404116. We show that the basic structure of this problem is that of finding eigenvectors of the matrix of second derivatives of the superpotential, and that many features of the results are determined by features of the generic ensemble of such matrices, the CI ensemble of Altland and Zirnbauer originating in mesoscopic physics. We study some simple examples in detail, exhibiting various factors which can favor low or high scale supersymmetry breaking.
295 citations
TL;DR: In this article, the problem of moduli stabilization in the presence of mobile branes has been studied in string theory and it is clear that the problem cannot be ignored in this context.
Abstract: The recent progress in embedding inflation in string theory has made it clear that the problem of moduli stabilization cannot be ignored in this context In many models a special role is played by the volume modulus, which is modified in the presence of mobile branes The challenge is to stabilize this modified volume while keeping the inflaton mass small compared to the Hubble parameter It is then crucial to know not only how the volume modulus is modified, but also to have control over the dependence of the potential on the inflaton field We address these questions within a simple setting: toroidal $\mathcal{N}=1$ type IIB orientifolds We calculate corrections to the superpotential and show how the holomorphic dependence on the properly modified volume modulus arises The potential then explicitly involves the inflaton, leaving room for lowering the inflaton mass through moderate fine-tuning of flux quantum numbers
280 citations
TL;DR: In this article, a dual formulation of the type-IIA theory on the T6/(Z2xZ2) orbifold and O6 orientifold, in the presence of D6-branes and general NSNS, RR and Scherk-Schwarz geometrical fluxes, is presented.
Abstract: We consider N=1 compactifications of the type-IIA theory on the T6/(Z2xZ2) orbifold and O6 orientifold, in the presence of D6-branes and general NSNS, RR and Scherk-Schwarz geometrical fluxes. Introducing a suitable dual formulation of the theory, we derive and solve the Bianchi identities, and show how certain combinations of fluxes can relax the constraints on D6-brane configurations coming from the cancellation of RR tadpoles. We then compute, via generalized dimensional reduction, the N=1, D=4 effective potential for the seven main moduli, and comment on the relation with truncated N=4 gaugings. As a byproduct, we obtain a general geometrical expression for the superpotential. We finally identify a family of fluxes, compatible with all Bianchi identities, that perturbatively stabilize all seven moduli in supersymmetric AdS4.
255 citations
TL;DR: In this paper, a non-critical string background in five and eight dimensions, holographically related to four-dimensional conformal field theories with = 0 and = 1 supersymmetries, was found.
Abstract: We find non-critical string backgrounds in five and eight dimensions, holographically related to four-dimensional conformal field theories with = 0 and = 1 supersymmetries. In the five-dimensional case we find an AdS5 background metric for a string model related to non-supersymmetric, conformal QCD with large number of colors and flavors and discuss the conjectured existence of a conformal window from the point of view of our solution. In the eight-dimensional string theory, we build a family of solutions of the form AdS5 ? 3 with 3 a squashed three-sphere. For a special value of the ratio Nf/Nc, the background can be interpreted as the supersymmetric near-horizon limit of a system of color and flavor branes on 1,3 times a known four-dimensional generalization of the cigar. The = 1 dual theory with fundamental matter should have an IR fixed point only for a fixed ratio Nf/Nc. General features of the string/gauge theory correspondence for theories with fundamental flavors are also addressed.
242 citations
TL;DR: In this paper, the physics of moduli fields are examined in the scenario where the gravitino is relatively heavy with mass of order 10 TeV, which is favored in view of the severe gravitinos problem.
Abstract: The physics of moduli fields is examined in the scenario where the gravitino is relatively heavy with mass of order 10 TeV, which is favored in view of the severe gravitino problem. The form of the moduli superpotential is shown to be determined, if one imposes a phenomenological requirement that no physical $CP$ phase arise in gaugino masses from conformal anomaly mediation. This bottom-up approach allows only two types of superpotential, each of which can have its origins in a fundamental underlying theory such as superstring. One superpotential is the sum of an exponential and a constant, which is identical to that obtained by Kachru et al. (KKLT), and the other is the racetrack superpotential with two exponentials. The general form of soft supersymmetry-breaking masses is derived, and the pattern of the superparticle mass spectrum in the minimal supersymmetric standard model is discussed with the KKLT-type superpotential. It is shown that the moduli mediation and the anomaly mediation make comparable contributions to the soft masses. At the weak scale, the gaugino masses are rather degenerate compared to the minimal supergravity, which bring characteristic features on the superparticle masses. In particular, the lightest neutralino, which often constitutes the lightest superparticle and thus a dark matter candidate, is a considerable admixture of gauginos and Higgsinos. We also find a small mass hierarchy among the moduli, gravitino, and superpartners of the standard-model fields. Cosmological implications of the scenario are briefly described.
231 citations
TL;DR: In this paper, the effects of adding RR, NS and metric fluxes on a T6/(Ω(−1)FLI3) type IIA orientifold were studied.
Abstract: We study the effects of adding RR, NS and metric fluxes on a T6/(Ω(−1)FLI3) type IIA orientifold. By using the effective flux-induced superpotential we obtain Minkowski or AdS vacua with broken or unbroken supersymmetry. In the Minkowski case some combinations of real moduli remain undetermined, whereas all can be stabilized in the AdS solutions. Many flux parameters are available which are unconstrained by RR tadpole cancellation conditions allowing to locate the minima at large volume and small dilaton. We also find that in AdS supersymmetric vacua with metric fluxes, the overall flux contribution to RR tadpoles can vanish or have opposite sign to that of D6-branes, allowing for new model-building possibilities. In particular, we construct the first = 1 supersymmetric intersecting D6-brane models with MSSM-like spectrum and with all closed string moduli stabilized. Some axion-like fields remain undetermined but they are precisely required to give Stuckelberg masses to (potentially anomalous) U(1) brane fields. We show that the cancellation of the Freed-Witten anomaly guarantees that the axions with flux-induced masses are orthogonal to those giving masses to the U(1)'s. Cancellation of such anomalies also guarantees that the D6-branes in our = 1 supersymmetric AdS vacua are calibrated so that they are forced to preserve one unbroken supersymmetry.
229 citations
TL;DR: In this paper, the effects of adding RR, NS and metric fluxes on a T^6/(\Omega (-1)^{F_L} I_3) Type IIA orientifold were studied.
Abstract: We study the effects of adding RR, NS and metric fluxes on a T^6/(\Omega (-1)^{F_L} I_3) Type IIA orientifold. By using the effective flux-induced superpotential we obtain Minkowski or AdS vacua with broken or unbroken supersymmetry. In the Minkowski case some combinations of real moduli remain undetermined, whereas all can be stabilized in the AdS solutions. Many flux parameters are available which are unconstrained by RR tadpole cancellation conditions allowing to locate the minima at large volume and small dilaton. We also find that in AdS supersymmetric vacua with metric fluxes, the overall flux contribution to RR tadpoles can vanish or have opposite sign to that of D6-branes, allowing for new model-building possibilities. In particular, we construct the first N=1 supersymmetric intersecting D6-brane models with MSSM-like spectrum and with all closed string moduli stabilized. Some axion-like fields remain undetermined but they are precisely required to give Stuckelberg masses to (potentially anomalous) U(1) brane fields. We show that the cancellation of the Freed-Witten anomaly guarantees that the axions with flux-induced masses are orthogonal to those giving masses to the U(1)'s. Cancellation of such anomalies also guarantees that the D6-branes in our N=1 supersymmetric AdS vacua are calibrated so that they are forced to preserve one unbroken supersymmetry.
222 citations
TL;DR: Using a Kaluza-Klein reduction of the fermionic part of the D-brane action, the authors compute D and F terms of the N = 1 effective action for generic Calabi-Yau orientifold compactifications in the presence of a space-time filling D7brane.
TL;DR: In this article, the authors consider the explicit example of F-theory on K3×K3 with D7 brane instantons and show that the resulting theories exhibit gaugino condensation, and generate a nonperturbative superpotential for Kahler moduli.
Abstract: Department of Physics and SLACStanford UniversityStanford, CA 94305/94309, USAThere are two known sources of nonperturbative superpotentials for Kahler moduli intype IIB orientifolds, or F-theory compactifications on Calabi-Yau fourfolds, with flux:Euclidean brane instantons and low-energy dynamics in D7 brane gauge theories. The firstclass of effects, Euclidean D3 branes which lift in M-theory to M5 branes wrapping divisorsof arithmetic genus 1 in the fourfold, is relatively well understood. The second class hasbeen less explored. In this paper, we consider the explicit example of F-theory on K3×K3with flux. The fluxes lift the D7 brane matter fields, and stabilize stacks of D7 branes atloci of enhanced gauge symmetry. The resulting theories exhibit gaugino condensation,and generate a nonperturbative superpotential for Kahler moduli. We describe how therelevant geometries in general contain cycles of arithmetic genus χ ≥ 1 (and how χ > 1divisors can contribute to the superpotential, in the presence of flux). This second class ofeffects is likely to be important in finding even larger classes of models where the KKLTmechanism of moduli stabilization can be realized. We also address various claims aboutthe situation for IIB models with a single Kahler modulus.July 2004
TL;DR: In this article, the SU(3) structure manifold was considered and the superpotential and the K??hler potential for the resulting SU(1) theories were derived and explicitly found N=1 supersymmetric minima.
Abstract: In this paper we consider compactifications of massive type IIA supergravity on manifolds with SU(3) structure. We derive the gravitino mass matrix of the effective four-dimensional N=2 theory and show that vacuum expectation values of the scalar fields naturally induce spontaneous partial supersymmetry breaking. We go on to derive the superpotential and the K??hler potential for the resulting N=1 theories. As an example we consider the SU(3) structure manifold SU(3)/U(1)??U(1) and explicitly find N=1 supersymmetric minima where all the moduli are stabilized at nontrivial values without the use of nonperturbative effects.
TL;DR: In this paper, the relative frequencies of vacua with vanishing superpotential W = 0 and with certain discrete symmetries were investigated in type IIB string theory in several simple but illustrative models.
Abstract: We study properties of flux vacua in type IIB string theory in several simple but illustrative models. We initiate the study of the relative frequencies of vacua with vanishing superpotential W = 0 and with certain discrete symmetries. For the models we investigate we also compute the overall rate of growth of the number of vacua as a function of the D3-brane charge associated to the fluxes, and the distribution of vacua on the moduli space. The latter two questions can also be addressed by the statistical theory developed by Ashok, Denef and Douglas, and our results are in good agreement with their predictions. Analysis of the first two questions requires methods which are more number-theoretic in nature. We develop some elementary techniques of this type, which are based on arithmetic properties of the periods of the compactification geometry at the points in moduli space where the flux vacua are located.
TL;DR: In this article, the N = 1 effective action for generic type IIA and type IIB Calabi-Yau orientifolds in the presence of background fluxes was derived by using a Kaluza-Klein reduction.
Abstract: This article first reviews the calculation of the N = 1 effective action for generic type IIA and type IIB Calabi-Yau orientifolds in the presence of background fluxes by using a Kaluza-Klein reduction. The Kahler potential, the gauge kinetic functions and the flux-induced superpotential are determined in terms of geometrical data of the Calabi-Yau orientifold and the background fluxes. As a new result, it is shown that the chiral description directly relates to Hitchin's generalized geometry encoded by special odd and even forms on a threefold, whereas a dual formulation with several linear multiplets makes contact to the underlying N = 2 special geometry. In type IIB setups, the flux-potentials can be expressed in terms of superpotentials, D-terms and, generically, a massive linear multiplet. The type IIA superpotential depends on all geometric moduli of the theory. It is reviewed, how type IIA orientifolds arise as a special limit of M-theory compactified on specific G2 manifolds by matching the effective actions. In a similar spirit type IIB orientifolds are shown to descend from F-theory on a specific class of Calabi-Yau fourfolds. In addition, mirror symmetry for Calabi-Yau orientifolds is briefly discussed and it is shown that the N = 1 chiral coordinates linearize the appropriate instanton actions.
TL;DR: In this article, the authors derive the effective N = 1 supergravity theory associated to the type IIA orientifolds with D6 branes, compactified on T6/(Z2× Z2).
Abstract: We illustrate the correspondence between the N =1 superstring compactifications with fluxes, the N = 4 gauged supergravities and the superpotential and Kahler potential of the effective N = 1 supergravity in four dimensions. In particular we derive, in the presence of general fluxes, the effective N = 1 supergravity theory associated to the type IIA orientifolds with D6 branes, compactified on T6/(Z2× Z2). We construct explicit examples with different features: in particular, new IIA no-scale models, new models with cosmological interest and a model which admits a supersymmetric AdS4 vacuum with all seven main moduli (S, TA, UA,A = 1,2,3) stabilized.
TL;DR: In this paper, the authors derive the effective N = 1 supergravity theory associated to the type IIA orientifolds with D6 branes, compactified on $T^6/(Z_2 \times Z_2) ).
Abstract: We illustrate the correspondence between the N=1 superstring compactifications with fluxes, the N=4 gauged supergravities and the superpotential and K\"ahler potential of the effective N=1 supergravity in four dimensions. In particular we derive, in the presence of general fluxes, the effective N=1 supergravity theory associated to the type IIA orientifolds with D6 branes, compactified on $T^6/(Z_2 \times Z_2)$. We construct explicit examples with different features: in particular, new IIA no-scale models, new models with cosmological interest and a model which admits a supersymmetric AdS$_4$ vacuum with all seven main moduli ($S, T_A, U_A,A=1,2,3$) stabilized.
TL;DR: In this paper, the authors examined recent work on compactifications of string theory with fluxes, where effective potentials for light moduli have been derived after integrating out moduli that are assumed to be heavy at the classical level, and then adding nonperturbative (NP) corrections to the superpotential.
TL;DR: In this paper, the fermion bilinear terms in the world volume action for a D3 brane in the presence of background flux were derived for six-dimensional compactifications on T6/Z2.
Abstract: We derive the fermion bilinear terms in the world volume action for a D3 brane in the presence of background flux. In six-dimensional compactifications non-perturbative corrections to the superpotential can arise from an euclidean D3-brane instanton wrapping a divisor in the internal space. The bilinear terms give rise to fermion masses and are important in determining these corrections. We find that the three-form flux generically breaks a U(1) subgroup of the structure group of the normal bundle of the divisor. In an example of compactification on T6/Z2, twelve of the sixteen zero modes originally present are lifted by the flux.
TL;DR: In this article, instanton generated superpotentials in Calabi-Yau orientifolds directly in type-IIB string theory were studied. And they were shown to be consistent with conclusions attainable via duality from an M-theory analysis.
Abstract: We study the problem of instanton generated superpotentials in Calabi-Yau orientifold compactifications directly in type-IIB string theory. To this end, we derive the Dirac equation on a euclidean D3 brane in the presence of background fluxes. We propose an index which governs whether the generation of a superpotential in the effective 4d theory by D3 brane instantons is possible. Applying the formalism to various classes of examples, including the K3 x T-2/Z(2) orientifold, in the absence and presence of fluxes, we show that our results are consistent with conclusions attainable via duality from an M-theory analysis.
TL;DR: In this paper, the minimal supersymmetric standard model tree level Higgs mass bound was increased to a value that is naturally larger than the LEP-II search constraint by adding to the superpotential a $\ensuremath{\lambda}S{H}{u}{H}_{d}$ term.
Abstract: In this paper we increase the minimal supersymmetric standard model tree level Higgs mass bound to a value that is naturally larger than the LEP-II search constraint by adding to the superpotential a $\ensuremath{\lambda}S{H}_{u}{H}_{d}$ term, as in the next to minimal supersymmetric standard model, and UV completing with new strong dynamics before $\ensuremath{\lambda}$ becomes nonperturbative. Unlike other models of this type, the Higgs fields remain elementary, alleviating the supersymmetric fine-tuning problem while maintaining unification in a natural way.
TL;DR: In this paper, the authors give a systematic derivation of the consistency conditions which constrain open-closed disk amplitudes of topological strings, including the A∞ relations and the homotopy versions of bulk-boundary crossing symmetry and Cardy constraint.
Abstract: We give a systematic derivation of the consistency conditions which constrain open-closed disk amplitudes of topological strings. They include the A∞ relations (which generalize associativity of the boundary product of topological field theory), as well as certain homotopy versions of bulk-boundary crossing symmetry and Cardy constraint. We discuss integrability of amplitudes with respect to bulk and boundary deformations, and write down the analogs of WDVV equations for the space-time superpotential. We also study the structure of these equations from a string field theory point of view. As an application, we determine the effective superpotential for certain families of D-branes in B-twisted topological minimal models, as a function of both closed and open string moduli. This provides an exact description of tachyon condensation in such models, which allows one to determine the truncation of the open string spectrum in a simple manner.
TL;DR: In this article, the Dirac equation on an M5 brane wrapped on a divisor in a Calabi-Yau fourfold in the presence of background flux was studied.
Abstract: We study the Dirac equation on an M5 brane wrapped on a divisor in a Calabi-Yau fourfold in the presence of background flux. We reduce the computation of the normal bundle U(1) anomaly to counting the solutions of a finite-dimensional linear system on cohomology. This system depends on the choice of flux. In an example, we find that the presence of flux changes the anomaly and allows instanton corrections to the superpotential which would otherwise be absent.
TL;DR: In this article, the structure of supersymmetric vacua in compactifications of the heterotic string on certain manifolds with SU(3) structure was analyzed and the effective theories associated with compactification on generalised half-flat manifolds were derived.
Abstract: In this paper we analyze the structure of supersymmetric vacua in compactifications of the heterotic string on certain manifolds with SU(3) structure. We first study the effective theories obtained from compactifications on half-flat manifolds and show that solutions which stabilise the moduli at acceptable values are hard to find. We then derive the effective theories associated with compactification on generalised half-flat manifolds. It is shown that these effective theories are consistent with four-dimensional N=1 supergravity and that the superpotential can be obtained by a Gukov-Vafa-Witten type formula. Within these generalised models, we find consistent supersymmetric (AdS) vacua at weak gauge coupling, provided we allow for general internal gauge bundles. In simple cases we perform a counting of such vacua and find that a fraction of about 1/1000 leads to a gauge coupling consistent with gauge unification.
TL;DR: In this paper, the effects of fluxes and gaugino condensation in heterotic supergravity were combined to find a new class of four-dimensional supersymmetric AdS4 compactifications on almost-Hermitian manifolds of SU(3) structure.
Abstract: Combining the effects of fluxes and gaugino condensation in heterotic supergravity, we use a ten-dimensional approach to find a new class of four-dimensional supersymmetric AdS4 compactifications on almost-Hermitian manifolds of SU(3) structure. Computation of the torsion allows a classification of the internal geometry, which for a particular combination of fluxes and condensate, is nearly Kahler. We argue that all moduli are fixed, and we show that the Kahler potential and superpotential proposed in the literature yield the correct AdS4 radius. In the nearly Kahler case, we are able to solve the H Bianchi identity using a nonstandard embedding. Finally, we point out subtleties in deriving the effective superpotential and understanding the heterotic supergravity in the presence of a gaugino condensate.
TL;DR: In this paper, the influence of four-form fluxes on the stabilization of the Kahler moduli in M-theory compactified on a Calabi-Yau fourfold was studied.
TL;DR: In this article, a new class of instanton effects in string compactifications that preserve only N = 1 supersymmetry in four dimensions is described. But the instantons can also contribute to new multi-fermion and higher-derivative F-terms in the low energy effective action.
Abstract: We describe a new class of instanton effects in string compactifications that preserve only N=1 supersymmetry in four dimensions. As is well-known, worldsheet or brane instantons in such a background can sometimes contribute to an effective superpotential for the moduli of the compactification. We generalize this phenomenon by showing that such instantons can also contribute to new multi-fermion and higher-derivative F-terms in the low-energy effective action. We consider in most detail the example of heterotic compactification on a Calabi-Yau threefold X with gauge bundle V, in which case we study worldsheet instanton effects that deform the complex structure of the moduli space associated to X and V. We also give new, slightly more economical derivations of some previous results about worldsheet instantons in Type IIA Calabi-Yau compactifications.
CERN1
TL;DR: In this article, the Scherk-Schwarz reduction of M-theory on twisted tori is analyzed in the presence of 4-form fluxes, and a detailed account of the effective supergravity with explicit expressions for the Kahler potential and the superpotential in terms of the fluxes and of the geometrical data of the internal manifold is provided.
Abstract: We analyse the 4-dimensional effective supergravity theories obtained from the Scherk-Schwarz reduction of M-theory on twisted 7-tori in the presence of 4-form fluxes. We implement the appropriate orbifold projection that preserves a G2-structure on the internal 7-manifold and truncates the effective field theory to an N = 1, D = 4 supergravity. We provide a detailed account of the effective supergravity with explicit expressions for the Kahler potential and the superpotential in terms of the fluxes and of the geometrical data of the internal manifold. Subsequently, we explore the landscape of vacua of M-theory compactifications on twisted tori, where we emphasize the role of geometric fluxes and discuss the validity of the bottom-up approach. Finally, by reducing along isometries of the internal 7-manifold, we obtain superpotentials for the corresponding type IIA backgrounds.
TL;DR: In this article, the problem of instanton generated superpotentials in Calabi-Yau orientifolds directly in type IIB string theory has been studied and the Dirac equation on a Euclidean D3 brane in the presence of background fluxes has been derived.
Abstract: We study the problem of instanton generated superpotentials in Calabi-Yau orientifold compactifications directly in type IIB string theory. To this end, we derive the Dirac equation on a Euclidean D3 brane in the presence of background fluxes. We propose an index which governs whether the generation of a superpotential in the effective 4d theory by D3 brane instantons is possible. Applying the formalism to various classes of examples, including the K3 x T^2/Z_2 orientifold, in the absence and presence of fluxes, we show that our results are consistent with conclusions attainable via duality from an M-theory analysis.
CERN1
TL;DR: In this paper, the Scherk-Schwarz reduction of M-theory on twisted 7-tori in the presence of 4-form fluxes has been analyzed and a detailed account of the Kaehler potential and the superpotential in terms of the fluxes and of the geometrical data of the internal manifold is provided.
Abstract: We analyse the 4-dimensional effective supergravity theories obtained from the Scherk--Schwarz reduction of M-theory on twisted 7-tori in the presence of 4-form fluxes. We implement the appropriate orbifold projection that preserves a G2-structure on the internal 7-manifold and truncates the effective field theory to an N=1, D=4 supergravity. We provide a detailed account of the effective supergravity with explicit expressions for the Kaehler potential and the superpotential in terms of the fluxes and of the geometrical data of the internal manifold. Subsequently, we explore the landscape of vacua of M-theory compactifications on twisted tori, where we emphasize the role of geometric fluxes and discuss the validity of the bottom-up approach. Finally, by reducing along isometries of the internal 7-manifold, we obtain superpotentials for the corresponding type IIA backgrounds.