Showing papers on "Superpotential published in 1997"
TL;DR: In this paper, the authors investigated topological properties of Calabi-Yau fourfolds and considered a wide class of explicit constructions in weighted projective spaces and more generally, toric varieties.
Abstract: We investigate topological properties of Calabi-Yau fourfolds and consider a wide class of explicit constructions in weighted projective spaces and, more generally, toric varieties. Divisors which lead to a non-perturbative superpotential in the effective theory have a very simple description in the toric construction. Relevant properties of them follow just by counting lattice points and can be also used to construct examples with negative Euler number. We study nets of transitions between cases with generically smooth elliptic fibres and cases with ADE gauge symmetries in the N=1 theory due to degenerations of the fibre over codimension one loci in the base. Finally we investigate the quantum cohomology ring of this fourfolds using Frobenius algebras.
223 citations
TL;DR: In this article, the dependence of superpotential terms in 4D F-theory on moduli parameters was studied, including the dependence on world-filling 3-brane positions and 2-form VEVs.
209 citations
TL;DR: In this paper, a local geometric model in terms of F-and M-theory compactification on Calabi-Yau 4-folds is constructed, which leads to N = 1 Yang-Mills theory in d = 4 and its reduction on a circle to d = 3.
206 citations
TL;DR: In this paper, the propagation of type I open superstrings on orbifolds with four non-compact dimensions and N = 1 supersymmetry was considered, and it was shown that consistency conditions, arising from tadpole cancellation and algebraic sources, require the existence of three sets of Dirichlet 5-branes.
167 citations
TL;DR: In this paper, the authors used brane configurations and SL(2, Z ) symmetry of the type IIB string to construct mirror N = 2 supersymmetric gauge theories in three dimensions.
166 citations
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TL;DR: In this article, it was shown that the fivebrane of type IIA theory can be used to give an exact low energy description of N=2 supersymmetric gauge theories in four dimensions.
Abstract: It has been known that the fivebrane of type IIA theory can be used to give an exact low energy description of N=2 supersymmetric gauge theories in four dimensions. We follow the recent M theory description by Witten and show that it can be used to study theories with N=1 supersymmetry. The N=2 supersymmetry can be broken to N=1 by turning on a mass for the adjoint chiral superfield in the N=2 vector multiplet. We construct the configuration of the fivebrane for both finite and infinite values of the adjoint mass. The fivebrane describes strong coupling dynamics of N=1 theory with SU(N_c) gauge group and N_f quarks. For N_c > N_f, we show how the brane configuration encodes the information of the Affleck-Dine-Seiberg superpotential. For N_c = and < N_f, we study the deformation space of the brane configuration and compare it with the moduli space of the N=1 theory. We find agreement with field theory results, including the quantum deformation of the moduli space at N_c = N_f. We also prove the type II s-rule in M theory and find new non-renormalization theorems for N=1 superpotentials.
162 citations
CERN1
TL;DR: In this article, the authors studied aspects of Calabi-Yau four-folds as compactification manifolds of F-theory, using mirror symmetry of toric hypersurfaces.
155 citations
TL;DR: In this article, it was shown that the fivebrane of type IIA theory can be used to give an exact low energy description of N=2 supersymmetric gauge theories in four dimensions.
Abstract: It has been known that the fivebrane of type IIA theory can be used to give an exact low energy description of N=2 supersymmetric gauge theories in four dimensions. We follow the recent M theory description by Witten and show that it can be used to study theories with N=1 supersymmetry. The N=2 supersymmetry can be broken to N=1 by turning on a mass for the adjoint chiral superfield in the N=2 vector multiplet. We construct the configuration of the fivebrane for both finite and infinite values of the adjoint mass. The fivebrane describes strong coupling dynamics of N=1 theory with SU(N_c) gauge group and N_f quarks. For N_c > N_f, we show how the brane configuration encodes the information of the Affleck-Dine-Seiberg superpotential. For N_c = and < N_f, we study the deformation space of the brane configuration and compare it with the moduli space of the N=1 theory. We find agreement with field theory results, including the quantum deformation of the moduli space at N_c = N_f. We also prove the type II s-rule in M theory and find new non-renormalization theorems for N=1 superpotentials.
140 citations
TL;DR: In this article, a tree-level neutrino mass originates from the superpotential in supersymmetric models and the suppression of neutrinos in comparison to the weak scale arises dynamically and need not be encoded in the super-potential.
130 citations
TL;DR: In this article, a systematic approach to confinement in N = 1 supersymmetric theories is developed, which identifies simple necessary conditions for theories to confine without chiral symmetry breaking and to generate a superpotential nonperturbatively.
Abstract: We develop a systematic approach to confinement in N=1 supersymmetric theories. We identify simple necessary conditions for theories to confine without chiral symmetry breaking and to generate a superpotential nonperturbatively (s-confine). Applying these conditions we identify all N=1 theories with a single gauge group and no tree-level superpotential which s-confine. We give a complete list of the confined spectra and superpotentials. Some of these theories are of great interest for model building. We give several new examples of models which break supersymmetry dynamically. {copyright} {ital 1997} {ital The American Physical Society}
125 citations
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TL;DR: In this article, the authors provide an introduction to the behavior of strongly-coupled supersymmetric gauge theories, and analyze the qualitative behavior of the simplest illustrative models, i.e., nonsymmetric QCD for N = 2 SU(2) and Yang-Mills theory.
Abstract: These lectures provide an introduction to the behavior of strongly-coupled supersymmetric gauge theories. After a discussion of the effective Lagrangian in nonsupersymmetric and supersymmetric field theories, I analyze the qualitative behavior of the simplest illustrative models. These include supersymmetric QCD for $N_f < N_c$, in which the superpotential is generated nonperturbatively, N=2 SU(2) Yang-Mills theory (the Seiberg-Witten model), in which the nonperturbative behavior of the effective coupling is described geometrically, and supersymmetric QCD for N_f large, in which the theory illustrates a non-Abelian generalization of electric-magnetic duality. [Lectures presented at the 1996 TASI Summer School, to appear in the proceedings.]
TL;DR: In this article, the theory of quantum cohomology may be generalized to "gravitational quantum cohology" by studying topological σ models coupled to two-dimensional gravity.
Abstract: We discuss how the theory of quantum cohomology may be generalized to "gravitational quantum cohomology" by studying topological σ models coupled to two-dimensional gravity. We first consider σ models defined on a general Fano manifold M (manifold with a positive first Chern class) and derive new recursion relations for its two-point functions. We then derive bi-Hamiltonian structures of the theories and show that they are completely integrable at least at the level of genus 0. We next consider the subspace of the phase space where only a marginal perturbation (with a parameter t) is turned on and construct Lax operators (superpotentials) L whose residue integrals reproduce correlation functions. In the case of M = CPN the Lax operator is given by and agrees with the potential of the affine Toda theory of the AN type. We also obtain Lax operators for various Fano manifolds; Grassmannians, rational surfaces, etc. In these examples the number of variables of the Lax operators is the same as the dimension of the original manifold. Our result shows that Fano manifolds exhibit a new type of mirror phenomenon where mirror partner is a noncompact Calabi–Yau manifold of the type of an algebraic torus C*N equipped with a specific superpotential.
TL;DR: In this paper, the authors consider type I string theory compactified on a {bold Z}{sub 7} orbifold and construct the heterotic dual, which matches the perturbative type I and heterotic tree-level massless spectra via giving certain scalars appropriate vacuum expectation values, VEVs, for this matching.
Abstract: In this paper we consider type I string theory compactified on a {bold Z}{sub 7} orbifold. The model has N=1 supersymmetry, a U(4){circle_times}U(4){circle_times}U(4){circle_times}SO(8) gauge group, and chiral matter. There are only D9-branes (for which we discuss tadpole cancellation conditions) in this model corresponding to a perturbative heterotic description in a certain region of the moduli space. We construct the heterotic dual, match the perturbative type I and heterotic tree-level massless spectra via giving certain scalars appropriate vacuum expectation values, VEVs, and point out the crucial role of the perturbative superpotential (on the heterotic side) for this matching. The relevant couplings in this superpotential turn out to be nonrenormalizable (unlike the Z-orbifold case discussed by Kakushadze, where Yukawa couplings sufficed for duality matching). We also discuss the role of the anomalous U(1) gauge symmetry present in both type I and heterotic models. In the perturbative regime we match the (tree-level) moduli spaces of these models. We point out possible generalizations of the {bold Z}{sub 3} and {bold Z}{sub 7} cases to include D5-branes which would help in understanding nonperturbative five-brane dynamics on the heterotic side. {copyright} {ital 1997} {ital The American Physical Society}
CERN1
TL;DR: In this paper, a universal superpotential is generated for the axion-dilaton superfield S. The resulting theory has a vacuum with 〈S〉 = 1, zero cosmological constant and a gravitino mass depending on the fifth radius as m32 ≈ R52/MPl.
TL;DR: In this paper, the authors consider the case when the domain walls are the BPS-saturated states, and 1/2 of supersymmetry is preserved, and several useful criteria that relate the preservation of 1 2 of the supersymmetric domain walls to the central extension appearing in the N = 1 superalgebras are established.
Abstract: Domain-wall solutions in four-dimensional supersymmetric field theories with distinct discrete vacuum states lead to the spontaneous breaking of supersymmetry, either completely or partially. We consider in detail the case when the domain walls are the BPS-saturated states, and 1/2 of supersymmetry is preserved. Several useful criteria that relate the preservation of 1/2 of supersymmetry on the domain walls to the central extension appearing in the N=1 superalgebras are established. We explain how the central extension can appear in N=1 supersymmetry and explicitly obtain the central charge in various models: the generalized Wess-Zumino models, and supersymmetric Yang-Mills theories with or without matter. The BPS-saturated domain walls satisfy the first-order differential equations which we call the creek equations, since they formally coincide with the (complexified) equations of motion of an analog high-viscosity fluid on a profile which is given by the superpotential of the original problem. Some possible applications are considered. We also briefly discuss BPS-saturated strings. {copyright} {ital 1997} {ital The American Physical Society}
TL;DR: In this paper, a supersymmetric scenario where R-parity is explicitly broken through a term bilinear in the lepton and Higgs superfields in the superpotential is investigated.
Abstract: We investigate a supersymmetric scenario where R-parity is explicitly broken through a term bilinear in the lepton and Higgs superfields in the superpotential. We show that keeping such a term alone can lead to trilinear interactions, similar to those that are parametrized by λand λ ′ in the literature, involving the physical fields. The upper limits of such interactions are predictable from the constraints on the parameter space imposed by the lepton masses and the neutrino mass limits. It is observed that thus the resulting trilinear interactions are restricted to values that are smaller than the existing bounds on most of the λ-and λ ′ -parameters. Some phenomenological consequences of such a scenario are discussed.
TL;DR: In this paper, the authors studied supersymmetric Sp(2N) gauge theories with matter in the antisymmetric tensor representation and F fundamentals, and obtained the theories with F < 6 which exhibit a host of interesting nonperturbative phenomena: quantum-deformed moduli spaces with N constraints, instanton-induced superpotentials and non-equivalent disjoint branches of moduli space.
Book•
31 Dec 1997
TL;DR: Part I: Nonconvexity in Engineering Applications; Part III: Superpotential Modelling and Optimization in Mechanics with and without ConveXity and Smoothness; Part IV: Computational Mechanics.
Abstract: Part I: Nonconvexity in Engineering Applications. 1. Nonconvexity in Engineering Applications. Part II: Applied Nonconvex Optimization Background. 2. Applied Nonconvex Optimization Background. Part III: Superpotential Modelling and Optimization in Mechanics with and without Convexity and Smoothness. 3. Convex Superpotential Problems. 4. Nonconvex Superpotential Problems. 5. Optimal Design Problems. Part IV: Computational Mechanics. Computer Implementation, Applications and Examples. 6. Computational Mechanics Algorithms. 7. Applications. Index.
TL;DR: In this paper, the authors give necessary criteria for $N\phantom{\rule{0ex}{0ex}} = \phantom {0ex} 0ex} 1$ supersymmetric theories to be in a smoothly confining phase without chiral symmetry breaking and with a dynamically generated superpotential.
Abstract: We give necessary criteria for $N\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1$ supersymmetric theories to be in a smoothly confining phase without chiral symmetry breaking and with a dynamically generated superpotential. Using our general arguments we find all such confining SU and Sp theories with a single gauge group and no tree-level superpotential.
TL;DR: In this paper, the SO(10) × U(1)A model was proposed to solve the doublet-triplet splitting problem via the missing VEV mechanism, and it was shown that all relevant GUT scales are related to a single dimensional parameter in the Higgs superpotential.
TL;DR: In this paper, the authors consider geometric engineering of N = 1 supersymmetric QFTs with matter in terms of a local model for compactification of F-theory on Calabi-Yau fourfold.
TL;DR: In this paper, the authors compare the modular superpotential with dual heterotic models and show how a heterotic super-potential matching the F theory computation is built up by world sheet instantons.
Abstract: We compare the N = 1F theory compactification of Donagi, Grassi and Witten with modular superpotential — and some closely related models — to dual heterotic models. We read of the F theory spectrum from the cohomology of the fourfold and discuss on the heterotic side the gauge bundle moduli sector (including the spectral surface) and the necessary fivebranes. Then we consider the N = 1 superpotential and show how a heterotic superpotential matching the F theory computation is built up by world sheet instantons. Finally we discuss how the original modular superpotential should be corrected by an additional modular correction factor, which on the F theory side matches nicely with a "curve counting function" for the del Pezzo surface. On the heterotic side we derive the same factor demanding correct T duality transformation properties of the superpotential.
TL;DR: In this article, the authors consider compactifications of type I strings on Abelian orbifolds and discuss the tadpole cancellation conditions for the general case with D9-branes only.
Abstract: In this paper we consider compactifications of type I strings on Abelian orbifolds. We discuss the tadpole cancellation conditions for the general case with D9-branes only. Such compactifications have (perturbative) heterotic duals which are also realized as orbifolds (with non-standard embedding of the gauge connection). The latter have extra twisted states that become massive once orbifold singularities are blown-up. This is due to the presence of perturbative heterotic superpotential with couplings between the extra twisted states, the orbifold blow-up modes, and (sometimes) untwisted matter fields. Anomalous U(1) (generically present in such models) also plays an important role in type I-heterotic (tree-level) duality matching. We illustrate these issues on a particular example of Z_3 \otimes Z_3 orbifold type I model (and its heterotic dual). The model has N=1 supersymmetry, U(4)^3 \otimes SO(8) gauge group, and chiral matter. We also consider compactifications of type I strings on Abelian orbifolds with both D9- and D5-branes. We discuss tadpole cancellation conditions for a certain class of such models. We illustrate the model building by considering a particular example of type I theory compactified on Z_6 orbifold. The model has N=1 supersymmetry, [U(6)\otimes U(6)\otimes U(4)]^2 gauge group, and chiral matter. This would correspond to a non-perturbative chiral vacuum from the heterotic point of view.
TL;DR: In this paper, it was shown that divisors contributing to the superpotential are always "exceptional" (in some sense) for the Calabi-Yau 4-fold X, also in M-theory.
Abstract: Each smooth elliptic Calabi-Yau 4-fold determines both a three-dimensional physical theory (a compactification of ``M-theory'') and a four-dimensional physical theory (using the ``F-theory'' construction). A key issue in both theories is the calculation of the ``superpotential''of the theory. We propose a systematic approach to identify these divisors, and derive some criteria to determine whether a given divisor indeed contributes. We then apply our techniques in explicit examples, in particular, when the base B of the elliptic fibration is a toric variety or a Fano 3-fold. When B is Fano, we show how divisors contributing to the superpotential are always "exceptional" (in some sense) for the Calabi-Yau 4-fold X. This naturally leads to certain transitions of X, that is birational transformations to a singular model (where the image of D no longer contributes) as well as certain smoothings of the singular model. If a smoothing exists, then the Hodge numbers change. We speculate that divisors contributing to the superpotential are always "exceptional" (in some sense) for X, also in M-theory. In fact we show that this is a consequence of the (log)-minimal model algorithm in dimension 4, which is still conjectural in its generality, but it has been worked out in various cases, among which toric varieties.
CERN1
TL;DR: In this article, the soft terms for the observable fields from wave-function renormalization are extracted from anomalous dimensions and beta functions, with no need to further compute any Feynman diagram, which greatly simplifies calculations which are rather involved if performed in terms of component fields.
Abstract: We show that in theories in which supersymmetry breaking is communicated by renormalizable perturbative interactions, it is possible to extract the soft terms for the observable fields from wave-function renormalization. Therefore all the information about soft terms can be obtained from anomalous dimensions and beta functions, with no need to further compute any Feynman diagram. This method greatly simplifies calculations which are rather involved if performed in terms of component fields. For illustrative purposes we reproduce known results of theories with gauge-mediated supersymmetry breaking. We then use our method to obtain new results of phenomenological importance. We calculate the next-to-leading correction to the Higgs mass parameters, the two-loop soft terms induced by messenger-matter superpotential couplings, and the soft terms generated by messengers belonging to vector supermultiplets.
01 Feb 1997
TL;DR: In this paper, a discussion of the effective Lagrangian in nonsupersymmetric and supersymmetric field theories is presented, and the qualitative behavior of the simplest illustrative models is analyzed.
Abstract: These lectures provide an introduction to the behavior of strongly-coupled supersymmetric gauge theories. After a discussion of the effective Lagrangian in nonsupersymmetric and supersymmetric field theories, the author analyzes the qualitative behavior of the simplest illustrative models. These include supersymmetric QCD for N{sub f} < N{sub c}, in which the superpotential is generated nonperturbatively, N = 2 SU(2) Yang-Mills theory (the Seiberg-Witten model), in which the nonperturbative behavior of the effect coupling is described geometrically, and supersymmetric QCD for N{sub f} large, in which the theory illustrates a non-Abelian generalization of electric-magnetic duality. 75 refs., 12 figs.
TL;DR: In this article, a superpotential is generated for the complex fields coming from $5d$ hypermultiplets, namely the dilaton $S$ and the complex structure moduli.
Abstract: We analyze in detail supersymmetry breaking by compactification of the fifth dimension in M-theory in the compactification pattern $11d \to 5d \to 4d$ and find that a superpotential is generated for the complex fields coming from $5d$ hypermultiplets, namely the dilaton $S$ and the complex structure moduli. Using general arguments it is shown that these fields are always stabilized such that they don't contribute to supersymmetry breaking, which is completely saturated by the Kahler moduli coming from vector multiplets.
It is shown that this mechanism is the strong-coupling analog of the Rohm-Witten quantization of the antisymmetric tensor field strength of string theories. The effect of a gaugino condensate on one of the boundaries is also considered.
TL;DR: In this paper, the authors compared the modular superpotential with dual heterotic models and showed how a heterotic super-potential matching the F-theory computation is built up by worldsheet instantons.
Abstract: We compare the N=1 F-theory compactification of Donagi, Grassi and Witten with modular superpotential - and some closely related models - to dual heterotic models. We read of the F-theory spectrum from the cohomology of the fourfold and discuss on the heterotic side the gauge bundle moduli sector (including the spectral surface) and the necessary fivebranes. Then we consider the N=1 superpotential and show how a heterotic superpotential matching the F-theory computation is built up by worldsheet instantons. Finally we discuss how the original modular superpotential should be corrected by an additional modular correction factor, which on the F-theory side matches nicely with a `curve counting function' for the del Pezzo surface. On the heterotic side we derive the same factor demanding correct T-duality transformation properties of the superpotential.
TL;DR: In this paper, it was shown that simple strongly coupled supersymmetric gauge theories with quantum moduli spaces can naturally lead to hybrid inflation, and the dynamical origin and scales of inflation and grand unification coincide.
TL;DR: In this paper, the moduli dependent effective potential arising from M-theory compactified on $M_4 \times X\times S^1 / Z_2 $, when one of the boundaries supports a strongly interacting gauge sector and induces gaugino condensation was derived.
Abstract: We derive the explicit form, and discuss some properties of the moduli dependent effective potential arising from M-theory compactified on $M_4 \times X\times S^1 / Z_2 $, when one of the boundaries supports a strongly interacting gauge sector and induces gaugino condensation. We discuss the relation between the explicit gaugino condensate and effective superpotential formulations and find interesting differences with respect to the situation known from the weakly coupled heterotic string case. The moduli dependence of the effective potential turns out to be more complicated than expected, and perhaps offers new clues to the stabilization problem.