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252
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
Parallel spinors and connections with skewsymmetric torsion in string theory
, 2008
"... We describe all almost contact metric, almost hermitian and G2structures admitting a connection with totally skewsymmetric torsion tensor, and prove that there exists at most one such connection. We investigate its torsion form, its Ricci tensor, the Dirac operator and the ∇parallel spinors. In p ..."
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Cited by 151 (7 self)
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We describe all almost contact metric, almost hermitian and G2structures admitting a connection with totally skewsymmetric torsion tensor, and prove that there exists at most one such connection. We investigate its torsion form, its Ricci tensor, the Dirac operator and the ∇parallel spinors. In particular, we obtain solutions of the type II string equations in dimension n = 5, 6 and 7.
Building a better racetrack
 JHEP 0406
"... We find IIb compactifications on CalabiYau orientifolds in which all Kähler moduli are stabilized, along lines suggested by Kachru, Kallosh, Linde and Trivedi. ..."
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Cited by 114 (8 self)
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We find IIb compactifications on CalabiYau orientifolds in which all Kähler moduli are stabilized, along lines suggested by Kachru, Kallosh, Linde and Trivedi.
Mirror symmetric SU(3)structure manifolds with NS fluxes
"... Unité mixte du CNRS et de l’EP, UMR 7644 ..."
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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
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.
A nogo theorem for string warped compactifications
, 2000
"... We give necessary conditions for the existence of perturbative heterotic and type II string warped compactifications preserving eight and four supersymmetries to four spacetime dimensions, respectively. In particular, we find that the only compactifications of heterotic string with the spin connecti ..."
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Cited by 60 (21 self)
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We give necessary conditions for the existence of perturbative heterotic and type II string warped compactifications preserving eight and four supersymmetries to four spacetime dimensions, respectively. In particular, we find that the only compactifications of heterotic string with the spin connection embedded in the gauge connection and type II strings are those on CalabiYau manifolds with constant dilaton. We obtain similar results for compactifications to six and to two dimensions.
The Srní lectures on nonintegrable geometries with torsion
 Arch. Math. (Brno
, 2006
"... Abstract. This review article intends to introduce the reader to nonintegrable geometric structures on Riemannian manifolds and invariant metric connections with torsion, and to discuss recent aspects of mathematical physics—in particular superstring theory—where these naturally appear. Connections ..."
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Cited by 58 (8 self)
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Abstract. This review article intends to introduce the reader to nonintegrable geometric structures on Riemannian manifolds and invariant metric connections with torsion, and to discuss recent aspects of mathematical physics—in particular superstring theory—where these naturally appear. Connections with skewsymmetric torsion are exhibited as one of the main tools to understand nonintegrable geometries. To this aim a a series of key examples is presented and successively dealt with using the notions of intrinsic torsion and characteristic connection of a Gstructure as unifying principles. The General Holonomy Principle bridges over to parallel objects, thus motivating the discussion of geometric stabilizers, with emphasis on spinors and differential forms. Several Weitzenböck formulas for Dirac operators associated with torsion connections enable us to discuss spinorial field equations, such as those governing the common sector of type II superstring theory.
Geometric model for complex nonKahler manifolds with SU(3) structure
 COMMUN. MATH. PHYS
, 2002
"... We propose a universal geometric construction of complex nonKähler manifolds with intrinsic SU(3) structure, used in supersymmetric string compactifications. All these manifolds are some T 2 fibrations over a CalabiYau base. We show that the conditions of N = 1 supersymmetry in the heterotic strin ..."
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Cited by 47 (0 self)
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We propose a universal geometric construction of complex nonKähler manifolds with intrinsic SU(3) structure, used in supersymmetric string compactifications. All these manifolds are some T 2 fibrations over a CalabiYau base. We show that the conditions of N = 1 supersymmetry in the heterotic string theory specify a subclass of manifolds that we constructed, which generalizes the examples known in the literature. Moreover, many known examples of internal manifolds in type II string compactifications can also be described in our construction, although supersymmetry restrictions of the geometry are not known yet. Mathematically, we construct complex, Hermitian nonKähler n + 1folds with a holomorphically trivial canonical bundle fibering over CalabiYau nfolds. We show that one can lift Special Lagrangian submanifolds and fibrations from the base CalabiYau to Special Lagrangian (calibrated) submanifolds and fibrations upstairs. We discuss in detail the Recently, 6dimensional nonKähler manifolds with SU(3) structure have attracted considerable