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184
Distributions of flux vacua
 JHEP
"... Abstract: We give results for the distribution and number of flux vacua of various types, supersymmetric and nonsupersymmetric, in IIb string theory compactified on CalabiYau manifolds. We compare this with related problems such as counting attractor points. Contents ..."
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Cited by 165 (16 self)
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Abstract: We give results for the distribution and number of flux vacua of various types, supersymmetric and nonsupersymmetric, in IIb string theory compactified on CalabiYau manifolds. We compare this with related problems such as counting attractor points. Contents
Fourdimensional String Compactifications with DBranes, Orientifolds and Fluxes
"... This review article provides a pedagogical introduction into various classes of chiral string compactifications to four dimensions with Dbranes and fluxes. The main concern is to provide all necessary technical tools to explicitly construct fourdimensional orientifold vacua, with the final aim to ..."
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Cited by 147 (18 self)
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This review article provides a pedagogical introduction into various classes of chiral string compactifications to four dimensions with Dbranes and fluxes. The main concern is to provide all necessary technical tools to explicitly construct fourdimensional orientifold vacua, with the final aim to come as close as possible to the supersymmetric Standard Model. Furthermore, we outline the available methods to derive the resulting fourdimensional effective action. Finally, we summarize recent attempts to address the
Nongeometric Flux Compactifications
, 2006
"... We investigate a simple class of type II string compactifications which incorporate nongeometric “fluxes” in addition to “geometric flux” and the usual Hfield and RR fluxes. These compactifications are nongeometric analogues of the twisted torus. We develop Tduality rules for NSNS geometric and ..."
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Cited by 129 (5 self)
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We investigate a simple class of type II string compactifications which incorporate nongeometric “fluxes” in addition to “geometric flux” and the usual Hfield and RR fluxes. These compactifications are nongeometric analogues of the twisted torus. We develop Tduality rules for NSNS geometric and nongeometric fluxes, which we use to construct a superpotential for the dimensionally reduced fourdimensional theory. The resulting structure is invariant under Tduality, so that the distribution of vacua in the IIA and IIB theories is identical when nongeometric fluxes are included. This gives a concrete framework in which to investigate the possibility that generic string compactifications may be nongeometric in any duality frame. The framework developed in this paper also provides some concrete hints for how mirror symmetry can be generalized to compactifications with arbitrary Hflux, whose mirrors are generically nongeometric.
Flux Compactifications of String Theory on Twisted Tori
, 2005
"... Global aspects of ScherkSchwarz dimensional reduction are discussed and it is shown that it can usually be viewed as arising from a compactification on the compact space obtained by identifying a (possibly noncompact) group manifold G under a discrete subgroup Γ, followed by a truncation. This all ..."
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Cited by 85 (4 self)
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Global aspects of ScherkSchwarz dimensional reduction are discussed and it is shown that it can usually be viewed as arising from a compactification on the compact space obtained by identifying a (possibly noncompact) group manifold G under a discrete subgroup Γ, followed by a truncation. This allows a generalisation of ScherkSchwarz reductions to string theory or Mtheory as compactifications on G/Γ, but only in those cases in which there is a suitable discrete subgroup of G. We analyse such compactifications with flux and investigate the gauge symmetry and its spontaneous breaking. We discuss the covariance under O(d,d), where d is the dimension of the group G, and the relation to reductions with duality twists. The compactified theories promote a subgroup of the O(d,d) that would arise from a toroidal reduction to a gauge symmetry, and we discuss the interplay between the gauge symmetry and the O(d,d, Z) Tduality group, suggesting the role that Tduality should play in such compactifications.
Fluxes, moduli fixing and MSSMlike vacua in a simple IIA orientifold
, 2005
"... We study the effects of adding RR, NS and metric fluxes on a T6 /(Ω(−1) FLI3) Type IIA orientifold. By using the effective fluxinduced superpotential we obtain Minkowski or AdS vacua with broken or unbroken supersymmetry. In the Minkowski case some combinations of real moduli remain undetermined, w ..."
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Cited by 82 (4 self)
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We study the effects of adding RR, NS and metric fluxes on a T6 /(Ω(−1) FLI3) Type IIA orientifold. By using the effective fluxinduced 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 D6branes, allowing for new modelbuilding possibilities. In particular, we construct the first N=1 supersymmetric intersecting D6brane models with MSSMlike spectrum and with all closed string moduli stabilized. Some axionlike fields remain undetermined but they are precisely required to give Stückelberg masses to (potentially anomalous) U(1) brane fields. We show that the cancellation of the FreedWitten anomaly guarantees that the axions with fluxinduced masses are orthogonal to those giving masses to the U(1)’s. Cancellation of such anomalies also guarantees that the D6branes in our N=1 supersymmetric AdS vacua are calibrated so that they are forced to preserve one unbroken supersymmetry.
BPS Action and Superpotential for Heterotic String Compactifications with Fluxes
, 2003
"... We consider N = 1 compactifications to four dimensions of heterotic string theory in the presence of fluxes. We show that up to order O (α ′2) the associated action can be written as a sum of squares of BPSlike quantities. In this way we prove that the equations of motion are solved by backgrounds ..."
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Cited by 81 (4 self)
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We consider N = 1 compactifications to four dimensions of heterotic string theory in the presence of fluxes. We show that up to order O (α ′2) the associated action can be written as a sum of squares of BPSlike quantities. In this way we prove that the equations of motion are solved by backgrounds which fulfill the supersymmetry conditions and the Bianchi identities. We also argue for the expression of the related superpotential and discuss the radial modulus
Topological Mtheory as Unification of Form Theories of Gravity
, 2004
"... We introduce a notion of topological Mtheory and argue that it provides a unification of form theories of gravity in various dimensions. Its classical solutions involve G2 holonomy metrics on 7manifolds, obtained from a topological action for a 3form gauge field introduced by Hitchin. We show tha ..."
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Cited by 70 (6 self)
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We introduce a notion of topological Mtheory and argue that it provides a unification of form theories of gravity in various dimensions. Its classical solutions involve G2 holonomy metrics on 7manifolds, obtained from a topological action for a 3form gauge field introduced by Hitchin. We show that by reductions of this 7dimensional theory one can classically obtain 6dimensional topological A and B models, the topological sector of loop quantum gravity in 4 dimensions, and ChernSimons gravity in 3 dimensions. We also find that the 7dimensional Mtheory perspective sheds some light on the fact that the topological string partition function is a wavefunction, as well as on Sduality between the A and B models. The degrees of freedom of the A and B models appear as conjugate variables in the 7dimensional theory. Finally, from the topological Mtheory perspective we find hints of an intriguing holographic link between nonsupersymmetric YangMills in
Constructing nongeometric vacua in string theory
 Nucl. Phys. B
, 2005
"... In this paper we investigate compactifications of the type II and heterotic string on fourdimensional spaces with nongeometric monodromies. We explicitly construct backgrounds which contain the “Duality Twists ” discussed by Dabholkar and Hull [1]. Similar constructions of nongeometric backgrounds ..."
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Cited by 68 (5 self)
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In this paper we investigate compactifications of the type II and heterotic string on fourdimensional spaces with nongeometric monodromies. We explicitly construct backgrounds which contain the “Duality Twists ” discussed by Dabholkar and Hull [1]. Similar constructions of nongeometric backgrounds have been discussed for type II strings by Hellerman, McGreevy, and Williams [2]. We find that imposing such monodromies projects out many moduli from the resulting vacua and argue that these backgrounds are the spacetime realizations of interpolating asymmetric orbifolds. April 20041. String theory and Geometry String theory, in spite of its aspirations as a fundamental theory of quantum gravity, is for the most part heavily reliant on classical notions of geometry. This being said, it is certainly true that strings and point particles probe classical geometries in dramatically different ways. It is wellknown that strings can resolve many of the singularities that plague classical and quantum gravity. Tduality establishes a remarkable equivalence between strings compactified on large tori with those compactified on small tori. In more general compactifications, one may take this a step further and relate geometries of
Supersymmetric sources, integrability and generalizedstructure compactifications
 J. High Energy Phys
"... Abstract: In the context of supersymmetric compactifications of type II supergravity to four dimensions, we show that orientifold sources can be compatible with a generalized SU(3) × SU(3)structure that is neither strictly SU(3) nor static SU(2). We illustrate this with explicit examples, obtained ..."
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Cited by 68 (12 self)
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Abstract: In the context of supersymmetric compactifications of type II supergravity to four dimensions, we show that orientifold sources can be compatible with a generalized SU(3) × SU(3)structure that is neither strictly SU(3) nor static SU(2). We illustrate this with explicit examples, obtained by suitably Tdualizing known solutions on the sixtorus. In addition we prove the following integrability statements, valid under certain mild assumptions: (a) for general type II supergravity backgrounds with orientifold and/or Dbrane generalizedcalibrated sources, the sourcecorrected Einstein and dilaton equations of motion follow automatically from the supersymmetry equations once the likewise sourcecorrected form equations of motion and Bianchi identities are imposed; (b) in the special case of supersymmetric compactifications to fourdimensional Minkowski space, the equations of motion of all fields, including the NSNS threeform, follow automatically once the supersymmetry and the Bianchi identities of the forms are imposed. Both (a) and (b) are equally valid whether the sources are smeared or localized. As a byproduct we obtain the calibration form for a spacefilling NS5brane.