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174
ElectricMagnetic duality and the geometric Langlands program
, 2006
"... The geometric Langlands program can be described in a natural way by compactifying on a Riemann surface C a twisted version of N = 4 super YangMills theory in four dimensions. The key ingredients are electricmagnetic duality of gauge theory, mirror symmetry of sigmamodels, branes, Wilson and ’t H ..."
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Cited by 294 (26 self)
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The geometric Langlands program can be described in a natural way by compactifying on a Riemann surface C a twisted version of N = 4 super YangMills theory in four dimensions. The key ingredients are electricmagnetic duality of gauge theory, mirror symmetry of sigmamodels, branes, Wilson and ’t Hooft operators, and topological field theory. Seemingly esoteric notions of the geometric Langlands program, such as Hecke
Topological sigmamodels with Hflux and twisted generalized complex manifolds
, 2008
"... We study the topological sector of N = 2 sigmamodels with Hflux. It has been known for a long time that the targetspace geometry of these theories is not Kähler and can be described in terms of a pair of complex structures, which do not commute, in general, and are parallel with respect to two di ..."
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Cited by 88 (4 self)
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We study the topological sector of N = 2 sigmamodels with Hflux. It has been known for a long time that the targetspace geometry of these theories is not Kähler and can be described in terms of a pair of complex structures, which do not commute, in general, and are parallel with respect to two different connections with torsion. Recently an alternative description of this geometry was found, which involves a pair of commuting twisted generalized complex structures on the target space. In this paper we define and study the analogues of A and Bmodels for N = 2 sigmamodels with Hflux and show that the results are naturally expressed in the language of twisted generalized complex geometry. For example, the space of topological observables is given by the cohomology of a Lie algebroid associated to one of the two twisted generalized complex structures. We determine the topological scalar product, which endows the algebra of observables with the structure of a Frobenius algebra. We also discuss mirror symmetry for twisted generalized CalabiYau manifolds.
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.
Supersymmetry breaking from a CalabiYau singularity
, 2005
"... We conjecture a geometric criterion for determining whether supersymmetry is spontaneously broken in certain string backgrounds. These backgrounds contain wrapped branes at CalabiYau singularites with obstructions to deformation of the complex structure. We motivate our conjecture with a particular ..."
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Cited by 70 (4 self)
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We conjecture a geometric criterion for determining whether supersymmetry is spontaneously broken in certain string backgrounds. These backgrounds contain wrapped branes at CalabiYau singularites with obstructions to deformation of the complex structure. We motivate our conjecture with a particular example: the Y 2,1 quiver gauge theory corresponding to a cone over the first del Pezzo surface, dP1. This setup can be analyzed using ordinary supersymmetric field theory methods, where we find that gaugino condensation drives a deformation of the chiral ring which has no solutions. We expect this breaking to be a general feature of any theory of branes at a singularity with a smaller number of possible deformations than independent anomalyfree fractional branes.
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
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.
An open string landscape
 JHEP
, 2005
"... Abstract: The effect of fluxes on open string moduli is studied by analyzing the constraints imposed by supersymmetry on Dbranes in type IIB flux backgrounds. We show that generically the conditions of supersymmetry cannot be maintained when moving along the geometrical moduli space of the brane, s ..."
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Cited by 56 (3 self)
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Abstract: The effect of fluxes on open string moduli is studied by analyzing the constraints imposed by supersymmetry on Dbranes in type IIB flux backgrounds. We show that generically the conditions of supersymmetry cannot be maintained when moving along the geometrical moduli space of the brane, so that open string moduli are lifted. In specific examples, we find that there is a disconnected and discrete set of supersymmetric solutions to the open string equations of motion, which extends the familiar closed string landscape to the open string sector. Permanent addressContents