Showing papers on "Superpotential published in 2001"
TL;DR: In this paper, the Chern-Simons/topological string duality in ordinary superstrings was shown to hold for generalized gauge systems with N=1 supersymmetry in four dimensions and superstrings propagating on noncompact Calabi-Yau manifolds with certain fluxes turned on.
Abstract: We embed the large N Chern–Simons/topological string duality in ordinary superstrings. This corresponds to a large N duality between generalized gauge systems with N=1 supersymmetry in four dimensions and superstrings propagating on noncompact Calabi–Yau manifolds with certain fluxes turned on. We also show that in a particular limit of the N=1 gauge theory system, certain superpotential terms in the N=1 system (including deformations if spacetime is noncommutative) are captured to all orders in 1/N by the amplitudes of noncritical bosonic strings propagating on a circle with self-dual radius. We also consider D-brane/anti-D-brane system wrapped over vanishing cycles of compact Calabi–Yau manifolds and argue that at large N they induce a shift in the background to a topologically distinct Calabi–Yau, which we identify as the ground state system of the brane/anti-brane system.
640 citations
TL;DR: In this article, a large N dual of 4d, N = 1 supersymmetric, SU(N) Yang-Mills with adjoint field Φ and arbitrary superpotential W(Φ) was proposed.
508 citations
TL;DR: In this article, the authors present an algorithm for extracting a consistent set of gauge theory data for an arbitrary toric variety whose singularity a D-brane probes, called Toric Duality.
385 citations
TL;DR: In this article, a large N dual of 4d, N=1 supersymmetric, SU(N) Yang-Mills with adjoint field and arbitrary superpotential W(\Phi) was proposed.
Abstract: We propose a large N dual of 4d, N=1 supersymmetric, SU(N) Yang-Mills with adjoint field \Phi and arbitrary superpotential W(\Phi). The field theory is geometrically engineered via D-branes partially wrapped over certain cycles of a non-trivial Calabi-Yau geometry. The large N, or low-energy, dual arises from a geometric transition of the Calabi-Yau, where the branes have disappeared and have been replaced by suitable fluxes. This duality yields highly non-trivial exact results for the gauge theory. The predictions indeed agree with expected results in cases where it is possible to use standard techniques for analyzing the strongly coupled, supersymmetric gauge theories. Moreover, the proposed large N dual provides a simpler and more unified approach for obtaining exact results for this class of supersymmetric gauge theories.
375 citations
TL;DR: In this article, the vacuum structure of type IIA/B Calabi-Yau string compactications to four dimensions in the presence of n-form H-fluxes is discussed.
307 citations
TL;DR: In this article, four N = 1 SU(N) 6 gauge theories, with bi-fundamental chiral matter and a superpotential, were studied and the spectrum of chiral operators in the gauge theories were compared to the D3-brane states in the AdS dual description.
Abstract: We study four N = 1 SU(N) 6 gauge theories, with bi-fundamental chiral matter and a superpotential. In the infrared, these gauge theories all realize the low-energy world-volume description of N coincident D3-branes transverse to the complex cone over a del Pezzo surface dP3 which is the blowup of P 2 at three generic points. Therefore, the four gauge theories are expected to fall into the same universality class | an example of a phenomenon that has been termed \toric duality". However, little independent evidence has been given that such theories are infrared-equivalent. In fact, we show that the four gauge theories are related by the N = 1 duality of Seiberg, vindicating this expectation. We also study holographic aspects of these gauge theories. In particular we relate the spectrum of chiral operators in the gauge theories to wrapped D3-brane states in the AdS dual description. We flnally demonstrate that the other known examples of toric duality are related by N = 1 duality, a fact which we conjecture holds generally.
248 citations
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TL;DR: In this article, the authors construct N=1 supersymmetric theories on worldvolumes of D5 branes wrapped around 2-cycles of threefolds which are A-D-E fibrations over a plane.
Abstract: We construct N=1 supersymmetric theories on worldvolumes of D5 branes wrapped around 2-cycles of threefolds which are A-D-E fibrations over a plane. We propose large N duals as geometric transitions involving blowdowns of two cycles and blowups of three-cycles. This yields exact predictions for a large class of N=1 supersymmetric gauge systems including U(N) gauge theories with two adjoint matter fields deformed by superpotential terms, which arise in A-D-E fibered geometries with non-trivial monodromies.
215 citations
TL;DR: In this paper, the Kaluza-Klein reduction of M-theory on warped Calabi-Yau fourfolds with non-trivial four-form flux turned on was performed.
183 citations
TL;DR: In this paper, the authors established general properties of supersymmetric flow equations and of the superpotential of five-dimensional N=2 gauged supergravity coupled to vector multiplets and hypermultiplets.
Abstract: We establish general properties of supersymmetric flow equations and of the superpotential of five-dimensional N=2 gauged supergravity coupled to vector multiplets and hypermultiplets. We provide necessary and sufficient conditions for BPS domain walls and find a set of algebraic attractor equations for N=2 critical points. As an example we describe in detail the gauging of the universal hypermultiplet and a vector multiplet. We study a two-parameter family of superpotentials with supersymmetric AdS critical points and we find, in particular, an N=2 embedding for the UV-IR solution of Freedman, Gubser, Pilch, and Warner of the N=8 theory. We comment on the relevance of these results for brane world constructions.
174 citations
TL;DR: In this article, the authors investigated solutions of type II supergravity which have the product R 1,3 ×M 6 structure with non-compact M 6 factor and which preserve at least four supersymmetries.
Abstract: We investigate solutions of type II supergravity which have the product R 1,3 ×M 6 structure with non-compact M 6 factor and which preserve at least four supersymmetries. In particular, we consider various conifolds and the N = 1 supersymmetric ‘NS5-brane wrapped on a 2-sphere’ solution recently discussed in hep-th/0008001. In all of these cases, we explicitly construct the complex structures, and the K¨ ahler and parallel (3, 0)-forms of the corresponding M 6 . In addition, we verify that the above solutions preserve, respectively, eight and four supersymmetries of the underlying type II theory. We also demonstrate that the ordinary and fractional D3-brane (5-brane wrapped on a 2-cycle) solutions on singular, resolved and deformed conifolds, and the (S-dual of) NS5-brane wrapped on 2-sphere can be obtained as special cases from a universal ansatz for the supergravity fields, i.e. from a single one-dimensional action governing their radial evolution. We show that like the 3-branes on conifolds, the NS5brane on a 2-sphere background can be found as a solution of a first-order system following from a superpotential.
171 citations
TL;DR: In this paper, the authors studied four N = 1 SU(N)^6 gauge theories, with bi-fundamental chiral matter and a superpotential, and showed that they are related by the N=1 duality of Seiberg, vindicating this expectation.
Abstract: We study four N=1 SU(N)^6 gauge theories, with bi-fundamental chiral matter and a superpotential. In the infrared, these gauge theories all realize the low-energy world-volume description of N coincident D3-branes transverse to the complex cone over a del Pezzo surface dP_3 which is the blowup of P^2 at three generic points. Therefore, the four gauge theories are expected to fall into the same universality class--an example of a phenomenon that has been termed "toric duality." However, little independent evidence has been given that such theories are infrared-equivalent.
In fact, we show that the four gauge theories are related by the N=1 duality of Seiberg, vindicating this expectation. We also study holographic aspects of these gauge theories. In particular we relate the spectrum of chiral operators in the gauge theories to wrapped D3-brane states in the AdS dual description. We finally demonstrate that the other known examples of toric duality are related by N=1 duality, a fact which we conjecture holds generally.
TL;DR: In this article, the authors consider the simplest and most economic version among the proposed nonminimal supersymmetric models, in which the $\ensuremath{\mu}$ parameter is promoted to a singlet superfield, whose self-couplings are all absent from the renormalizable superpotential.
Abstract: We consider the simplest and most economic version among the proposed nonminimal supersymmetric models, in which the $\ensuremath{\mu}$ parameter is promoted to a singlet superfield, whose self-couplings are all absent from the renormalizable superpotential. Such a particularly simple form of the renormalizable superpotential may be enforced by discrete R symmetries which are extended to the gravity-induced nonrenormalizable operators as well. We show explicitly that within the supergravity-mediated supersymmetry-breaking scenario, the potentially dangerous divergent tadpoles associated with the presence of the gauge singlet first appear at loop levels higher than 5 and therefore do not destabilize the gauge hierarchy. The model provides a natural explanation for the origin of the $\ensuremath{\mu}$ term, without suffering from the visible axion or the cosmological domain-wall problem. Focusing on the Higgs sector of this minimal nonminimal supersymmetric standard model, we calculate its effective Higgs potential by integrating out the dominant quantum effects due to top squarks. We then discuss the phenomenological implications of the Higgs scalars predicted by the theory for the present and future high-energy colliders. In particular, we find that our new minimal nonminimal supersymmetric model can naturally accommodate a relatively light charged Higgs boson, with a mass close to the present experimental lower bound.
TL;DR: In this article, the Affleck-Dine baryogenesis in the minimal supersymmetric standard model with gauge-mediated supersymmetry breaking is considered and a very narrow region in the parameter space is obtained to explain the baryon number of the universe.
Abstract: We consider the Affleck-Dine baryogenesis comprehensively in the minimal supersymmetric standard model with gauge-mediated supersymmetry breaking. Considering the high temperature effects, we see that the Affleck-Dine field is naturally deformed into the form of the Q ball. In the natural scenario where the initial amplitude of the field and the A terms are both determined by the nonrenormalizable superpotential, we obtain only a very narrow allowed region in the parameter space in order to explain the baryon number of the universe for the case that the Q-ball formation occurs just after baryon number production. Moreover, most of the parameter sets suited have already been excluded by current experiments. We also find new situations in which the Q-ball formation takes place rather late compared with baryon number creation. This situation is more preferable, since it allows a wider parameter region for naturally consistent scenarios, although it is still difficult to realize in the actual cosmological scenario.
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TL;DR: In this article, the authors study the open string extension of the mirror map for N=1 supersymmetric type II vacua with D-branes on non-compact Calabi-Yau manifolds.
Abstract: We study the open string extension of the mirror map for N=1 supersymmetric type II vacua with D-branes on non-compact Calabi-Yau manifolds. Its definition is given in terms of a system of differential equations that annihilate certain period and chain integrals. The solutions describe the flat coordinates on the N=1 parameter space, and the exact disc instanton corrected superpotential on the D-brane world-volume. A gauged linear sigma model for the combined open-closed string system is also given. It allows to use methods of toric geometry to describe D-brane phase transitions and the N=1 K\"ahler cone. Applications to a variety of D-brane geometries are described in some detail.
TL;DR: In this paper, the nonlinear supersymmetry of one-dimensional systems is investigated in the context of the quantum anomaly problem, and the most general one-parametric Calogero-like solution with the second order supercharges is found.
TL;DR: In this paper, the authors studied the phenomenology of a new minimally extended supersymmetric standard model (nMSSM) where a gauge singlet superfield is added to the MSSM spectrum.
Abstract: We study the phenomenology of a new minimally extended supersymmetric standard model (nMSSM) where a gauge singlet superfield is added to the MSSM spectrum. The superpotential of this model contains no dimensionful parameters, thus solving the ? problem of the MSSM. A global discrete R symmetry, forbidding the cubic singlet self-interaction, imposed on the complete theory, guarantees its stability with respect to generated higher-order tadpoles of the singlet and solves both the domain wall and Peccei-Quinn axion problems. We give the free parameters of the model and display some general constraints on them. Particular attention is devoted to the neutralino sector where a (quasipure) singlino appears to be always the LSP of the model, leading to additional cascades, involving the NLSP ? LSP transition, compared with the MSSM. We then present the upper bounds on the masses of the lightest and next-to-lightest—when the lightest is an invisible singlet—CP-even Higgs bosons, including the full one-loop and dominant two-loop corrections. These bounds are found to be much higher than the equivalent ones in the MSSM. Finally, we discuss some phenomenological implications for the Higgs sector of the nMSSM in Higgs boson production at future hadron colliders.
TL;DR: In this article, the authors extend the large N duality of four dimensional = 1 supersymmetric Yang-Mills theory with additional chiral fields and arbitrary superpotential to the case of SO/Sp gauge groups.
Abstract: We extend the large N duality of four dimensional = 1 supersymmetric Yang-Mills theory with additional chiral fields and arbitrary superpotential recently proposed by Cachazo, Intriligator and Vafa to the case of SO/Sp gauge groups. By orientifolding the geometric transition, we investigate a large N duality between = 1, SO/Sp supersymmetric theories with arbitrary superpotential and an abelian = 2 theory with supersymmetry broken to = 1 by electric and magnetic Fayet-Iliopoulos terms.
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TL;DR: In this paper, the exact N = 1 superpotential of a class of 4D string compactifications is computed by the closed topological string compactified to two dimensions, which is used to define a special geometry for N=1 mirror symmetry.
Abstract: We show that the exact N=1 superpotential of a class of 4d string compactifications is computed by the closed topological string compactified to two dimensions. A relation to the open topological string is used to define a special geometry for N=1 mirror symmetry. Flat coordinates, an N=1 mirror map for chiral multiplets and the exact instanton corrected superpotential are obtained from the periods of a system of differential equations. The result points to a new class of open/closed string dualities which map individual string world-sheets with boundary to ones without. It predicts an mathematically unexpected coincidence of the closed string Gromov-Witten invariants of one Calabi-Yau geometry with the open string invariants of the dual Calabi-Yau.
TL;DR: In this article, a formalism for calculating the open supermembrane contribution to the nonperturbative superpotential of moduli in heterotic M-theory is presented.
Abstract: A formalism for calculating the open supermembrane contribution to the non-perturbative superpotential of moduli in heterotic M-theory is presented. This is explicitly applied to the Calabi-Yau (1,1)-moduli and the separation modulus of the end-of-the-world BPS three-branes, whose non-perturbative superpotential is computed. The role of gauge bundles on the boundaries of the open supermembranes is discussed in detail, and a topological criterion presented for the associated superpotential to be non-vanishing.
TL;DR: In this paper, a formalism for calculating the open supermembrane contribution to the nonperturbative superpotential of moduli in heterotic M-theory is presented.
TL;DR: In this paper, the authors studied the superpotential of scalar potential of RG flows in three-dimensional boundary conformal field theory from UV fixed point to IR fixed point, and derived the first-order BPS domain-wall solutions.
TL;DR: In this article, the authors studied the effective low energy supergravity of the strongly coupled heterotic string compactified on a Calabi-Yau 3-fold with generic E 8 × E 8 gauge bundle.
TL;DR: Surprisingly, the pattern of grand unified theory scale soft supersymmetry breaking masses are close to those found in the context of inverted hierarchy models.
Abstract: Supersymmetric grand unified models based on $\mathrm{SO}(10)$ gauge symmetry have many desirable features, including the unification of Yukawa couplings. Including $D$-term contributions to scalar masses arising from the breakdown of $\mathrm{SO}(10)$, Yukawa coupling unification only to $30%$ can be achieved in models with a positive superpotential Higgs mass. The superparticle mass spectrum is highly constrained and yields relatively light top squarks and charginos. Surprisingly, the pattern of grand unified theory scale soft supersymmetry breaking masses are close to those found in the context of inverted hierarchy models.
TL;DR: In this article, the Coulomb-Higgs duality of = 2 supersymmetric abelian Chern-Simons theories in 2+1 dimensions was studied by compactifying dual pairs on a circle of radius R and comparing the resulting = (2,2) theories in 1+ 1 dimensions.
Abstract: We study the Coulomb-Higgs duality of = 2 supersymmetric abelian Chern-Simons theories in 2+1 dimensions, by compactifying dual pairs on a circle of radius R and comparing the resulting = (2,2) theories in 1+1 dimensions. Below the compactification scale, the theory on the Higgs branch reduces to the non-linear sigma model on a toric manifold. In the dual theory on the Coulomb branch, the Kaluza-Klein modes generate an infinite tower of contributions to the superpotential. After resummation, in the limit R?0 the superpotential becomes that of the Landau-Ginzburg model which is the two-dimensional mirror of the toric sigma model. We further examine the conjecture of all-scale three-dimensional mirror symmetry and observe that it is consistent with mirror symmetry in 1+1 dimensions.
TL;DR: In this paper, the deformation of S 7 gives rise to nontrivial renormalization group flow in a three-dimensional boundary super conformal field theory from N =8, SO(8) invariant UV fixed point to N =2, SU(3)×U(1) IR fixed point.
TL;DR: In this paper, the authors extend the large N duality of four dimensional N=1 supersymmetric Yang-Mills theory with additional chiral fields and arbitrary superpotential to the case of SO/Sp gauge groups.
Abstract: We extend the large N duality of four dimensional N=1 supersymmetric Yang-Mills theory with additional chiral fields and arbitrary superpotential recently proposed by Cachazo, Intriligator and Vafa to the case of SO/Sp gauge groups By orientifolding the geometric transition, we investigate a large N duality between N=1, SO/Sp supersymmetric theories with arbitrary superpotential and an Abelian N=2 theory with supersymmetry broken to N=1 by electric and magnetic Fayet-Iliopoulos terms
TL;DR: In this article, the authors show that the well-known N = 2 heterotic/type II string-string duality still holds for a subset of all possible fluxes, namely those which arise from six-dimensional gauge fields with internal magnetic flux on the common two-sphere P1, which is the base space of the type II K3-fibration.
Abstract: In this paper we consider heterotic compactifications on K3 x T2 as well as type II compactifications on K3-fibred Calabi-Yau spaces with certain fluxes for the gauge and RR field strengths F and H turned on. By providing an identification of corresponding fluxes we show that the well-known N=2 heterotic/type II string-string duality still holds for a subset of all possible fluxes, namely those which arise from six-dimensional gauge fields with internal magnetic flux on the common two-sphere P1, which is the base space of the type II K3-fibration. On the other hand, F- and H-fluxes without P1-support, such as heterotic F-fluxes on the torus T2 or type II H-fluxes on cycles of the K3-fibre cannot be matched in any simple way, which is a challenge for heterotic/type II string-string duality. Our analysis is based on the comparison of terms in the effective low-energy heterotic and type II actions which are induced by the fluxes, such as the Green-Schwarz couplings related to flux-induced U(1) anomalies, the effective superpotential and the Fayet-Iliopoulos scalar potential.
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TL;DR: In this article, large N dualities for a general class of N=1 theories realized on type IIB D5 branes wrapping 2-cycles of local Calabi-Yau threefolds or as effective field theories on D4 branes in type IIA brane configurations were studied.
Abstract: We study large N dualities for a general class of N=1 theories realized on type IIB D5 branes wrapping 2-cycles of local Calabi-Yau threefolds or as effective field theories on D4 branes in type IIA brane configurations. We completely solve the issue of the classical moduli space for N=2, U(N_1)x ... x U(N_n) theories deformed by a general superpotential for the adjoint and bifundamental fields. The N=1 geometries in type IIB and its T-dual brane configurations are presented and they agree with the field theory analysis. We investigate the geometric transitions in the ten dimensional theories as well as in M-theory. Strong coupling effects in field theory are analyzed in the deformed geometry with fluxes. Gluino condensations are identified the normalizable deformation parameters while the vacuum expectation values of the bifundamental fields are with the non-normalizable ones. By lifting to M theory, we get a transition from finite coverings of non-hyperelliptic curves to non-hyperelliptic curves. We also discuss orientifold theories, Seiberg dualities and mirror symmetries.
TL;DR: In this paper, a supersymmetric M3-brane solution of the complete Ricci-flat metric of G_2 holonomy on R^4\times S^3 to a family with a non-trivial parameter is given.
Abstract: We obtain a generalisation of the original complete Ricci-flat metric of G_2 holonomy on R^4\times S^3 to a family with a non-trivial parameter \lambda. For generic \lambda the solution is singular, but it is regular when \lambda={-1,0,+1}. The case \lambda=0 corresponds to the original G_2 metric, and \lambda ={-1,1} are related to this by an S_3 automorphism of the SU(2)^3 isometry group that acts on the S^3\times S^3 principal orbits. We then construct explicit supersymmetric M3-brane solutions in D=11 supergravity, where the transverse space is a deformation of this class of G_2 metrics. These are solutions of a system of first-order differential equations coming from a superpotential. We also find M3-branes in the deformed backgrounds of new G_2-holonomy metrics that include one found by A. Brandhuber, J. Gomis, S. Gubser and S. Gukov, and show that they also are supersymmetric.
TL;DR: In this paper, the dynamics of a large class of N-1 quiver theories, geometrically realized by type IIB D-brane probes wrapping cycles of local Calabi-Yau threefolds, are studied.
Abstract: We study the dynamics of a large class of N=1 quiver theories, geometrically realized by type IIB D-brane probes wrapping cycles of local Calabi-Yau threefolds. These include N=2 (affine) A-D-E quiver theories deformed by superpotential terms, as well as chiral N=1 quiver theories obtained in the presence of vanishing 4-cycles inside a Calabi-Yau. We consider the various possible geometric transitions of the 3-fold and show that they correspond to Seiberg-like dualities (represented by Weyl reflections in the A-D-E case or `mutations' of bundles in the case of vanishing 4-cycles) or large N dualities involving gaugino condensates (generalized conifold transitions). Also duality cascades are naturally realized in these classes of theories, and are related to the affine Weyl group symmetry in the A-D-E case.