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32
Gauge theories from toric geometry and brane tilings
, 2005
"... We provide a general set of rules for extracting the data defining a quiver gauge theory from a given toric Calabi–Yau singularity. Our method combines information from the geometry and topology of Sasaki–Einstein manifolds, AdS/CFT, dimers, and brane tilings. We explain how the field content, quan ..."
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Cited by 147 (25 self)
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We provide a general set of rules for extracting the data defining a quiver gauge theory from a given toric Calabi–Yau singularity. Our method combines information from the geometry and topology of Sasaki–Einstein manifolds, AdS/CFT, dimers, and brane tilings. We explain how the field content, quantum numbers, and superpotential of a superconformal gauge theory on D3–branes probing a toric Calabi–Yau singularity can be deduced. The infinite family of toric singularities with known horizon Sasaki–Einstein manifolds La,b,c is used to illustrate these ideas. We construct the corresponding quiver gauge theories, which may be fully specified by giving a tiling of the plane by hexagons with certain gluing rules. As checks of this construction, we perform amaximisation as well as Zminimisation to compute the exact Rcharges of an arbitrary such quiver. We also examine a number of examples in detail, including the infinite subfamily La,b,a, whose smallest member is the
Fractional Branes and Dynamical Supersymmetry Breaking
, 2005
"... We study the dynamics of fractional branes at toric singularities, including cones over del Pezzo surfaces and the recently constructed Y p,q theories. We find that generically the field theories on such fractional branes show dynamical supersymmetry breaking, due to the appearance of nonperturba ..."
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Cited by 43 (6 self)
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We study the dynamics of fractional branes at toric singularities, including cones over del Pezzo surfaces and the recently constructed Y p,q theories. We find that generically the field theories on such fractional branes show dynamical supersymmetry breaking, due to the appearance of nonperturbative superpotentials. In special cases, one recovers the known cases of supersymmetric infrared behaviors, associated to SYM confinement (mapped to complex deformations of the dual geometries, in the gauge/string correspondence sense) or N = 2 fractional branes. In the supersymmetry breaking cases, when the dynamics of closed string moduli at the singularity is included, the theories show a runaway behavior (involving moduli such as FI terms or equivalently dibaryonic operators), rather than stable nonsupersymmetric minima. We comment on the implications of this gauge theory behavior for the infrared smoothing of the dual warped throat solutions with 3form fluxes, describing duality cascades ending in such field theories. We finally provide a description of the different fractional branes in the recently introduced brane tiling configurations.
Quiver gauge theories at resolved and deformed singularities using dimers
 JHEP
"... The gauge theory on a set of D3branes at a toric CalabiYau singularity can be encoded in a tiling of the 2torus denoted dimer diagram (or brane tiling). We use these techniques to describe the effect on the gauge theory of geometric operations partially smoothing the singularity at which D3brane ..."
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Cited by 21 (3 self)
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The gauge theory on a set of D3branes at a toric CalabiYau singularity can be encoded in a tiling of the 2torus denoted dimer diagram (or brane tiling). We use these techniques to describe the effect on the gauge theory of geometric operations partially smoothing the singularity at which D3branes sit, namely partial resolutions and complex deformations. More specifically, we describe the effect of arbitrary partial resolutions, including those which split the original singularity into two separated. The gauge theory correspondingly splits into two sectors (associated to branes in either singularity) decoupled at the level of massless states. We also describe the effect of complex deformations, associated to geometric transitions triggered by the presence of fractional branes with confinement in their infrared. We provide tools to The study of the N = 1 supersymmetric gauge theory on a stack of D3branes probing a CalabiYau threefold conical singularity is a fruitful source of new insights into brane dynamics [1, 2], the AdS/CFT correspondence [3], and its extensions to nonconformal situations by the addition of fractional branes [4].
Sequestering in string theory
 JHEP 0710 (2007) 013 [arXiv:hepth/0703105
"... We study sequestering, a prerequisite for flavorblind supersymmetry breaking in several highscale mediation mechanisms, in compactifications of type IIB string theory. We find that although sequestering is typically absent in unwarped backgrounds, strongly warped compactifications do readily seque ..."
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Cited by 15 (4 self)
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We study sequestering, a prerequisite for flavorblind supersymmetry breaking in several highscale mediation mechanisms, in compactifications of type IIB string theory. We find that although sequestering is typically absent in unwarped backgrounds, strongly warped compactifications do readily sequester. The AdS/CFT dual description in terms of conformal sequestering plays an important role in our analysis, and we establish how sequestering works both on the gravity side and on the gauge theory side. We pay special attention to subtle compactification effects that can disrupt sequestering. Our result is a step toward realizing an appealing pattern of soft terms in a KKLT compactification.
Quantum Deformations from Toric Geometry
, 2005
"... We will demonstrate how calculations in toric geometry can be used to compute quantum corrections to the relations in the chiral ring for certain gauge theories. We focus on the gauge theory of the del Pezzo 2, and derive the chiral ring relations and quantum deformations to the vacuum moduli spac ..."
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Cited by 12 (1 self)
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We will demonstrate how calculations in toric geometry can be used to compute quantum corrections to the relations in the chiral ring for certain gauge theories. We focus on the gauge theory of the del Pezzo 2, and derive the chiral ring relations and quantum deformations to the vacuum moduli space using AffleckDineSeiberg superpotential arguments. Then we calculate the versal deformation to the corresponding toric geometry using a method due to Altmann, and show that the result is equivalent to the deformation calculated using gauge theory. In an appendix we will apply this technique to a few other examples. This is a new method for understanding the infrared dynamics of certain quiver gauge theories.
Deformations of toric singularities and fractional branes
 JHEP 0610 (2006) 080 [arXiv:hepth/0603253
"... Fractional branes added to a large stack of D3branes at the singularity of a CalabiYau cone modify the quiver gauge theory breaking conformal invariance and leading to different kinds of IR behaviors. For toric singularities admitting complex deformations we propose a simple method that allows to ..."
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Cited by 12 (1 self)
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Fractional branes added to a large stack of D3branes at the singularity of a CalabiYau cone modify the quiver gauge theory breaking conformal invariance and leading to different kinds of IR behaviors. For toric singularities admitting complex deformations we propose a simple method that allows to compute the anomaly free rank distributions in the gauge theory corresponding to the fractional deformation branes. This algorithm fits Altmann’s rule of decomposition of the toric diagram into a Minkowski sum of polytopes. More generally we suggest how different IR behaviors triggered by fractional branes can be classified by looking at suitable weights associated with the external legs of the (p,q) web. We check the proposal on many examples and match in some interesting cases the moduli space of the gauge theory with the deformed geometry.
Short distance properties of cascading gauge theories
 JHEP
, 2006
"... We study the short distance (large momentum) properties of correlation functions of cascading gauge theories by performing a treelevel computation in their dual gravitational background. We prove that these theories are holographically renormalizable; the correlators have only analytic ultraviolet ..."
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Cited by 10 (4 self)
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We study the short distance (large momentum) properties of correlation functions of cascading gauge theories by performing a treelevel computation in their dual gravitational background. We prove that these theories are holographically renormalizable; the correlators have only analytic ultraviolet divergences, which may be removed by appropriate local counterterms. We find that npoint correlation functions of properly normalized operators have the expected scaling in the semiclassical gravity (large N) limit: they scale as N 2−n eff with Neff ∝ ln(k/Λ) where k is a typical momentum. Our analysis thus confirms the interpretation of the cascading gauge theories as renormalizable fourdimensional quantum field theories with an effective number of degrees of freedom which logarithmically increases with the energy. August 20061 Introduction and summary Cascading gauge theories were discovered in [1–3] (see [4, 5] for reviews) by looking
The dual superconformal theory for L p,q,r manifolds
 JHEP 0509
"... We present the superconformal gauge theory living on the worldvolume of D3 branes probing the toric singularities with horizon the recently discovered SasakiEinstein manifolds L p,q,r. Various checks of the identification are made by comparing the central charge and the Rcharges of the chiral fie ..."
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Cited by 5 (0 self)
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We present the superconformal gauge theory living on the worldvolume of D3 branes probing the toric singularities with horizon the recently discovered SasakiEinstein manifolds L p,q,r. Various checks of the identification are made by comparing the central charge and the Rcharges of the chiral fields with the information that can be extracted from toric geometry. Fractional branes are also introduced and the physics of the associated duality cascade discussed.
Gauge theories from D7branes over vanishing 4cycles
"... Abstract: We study quiver gauge theories on D7branes wrapped over vanishing holomorphic4cycles. WeinvestigatehowtoincorporateO7planesand/orflavorD7branes, which are necessary to cancel anomalies. These theories are chiral, preserve foursupercharges and exhibit very richinfrareddynamics. Geometric ..."
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Cited by 4 (1 self)
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Abstract: We study quiver gauge theories on D7branes wrapped over vanishing holomorphic4cycles. WeinvestigatehowtoincorporateO7planesand/orflavorD7branes, which are necessary to cancel anomalies. These theories are chiral, preserve foursupercharges and exhibit very richinfrareddynamics. Geometrictransitionsand duality in the presence of Oplanes are analyzed. We study the Higgs branch of these quiver theories, showing the emergence of fuzzy internal dimensions. This branch is related to noncommutative instantons on the divisor wrapped by the sevenbranes. Our results have a natural application to the recently introduced F(uzz) limit of Ftheory.