Showing papers on "Superpotential published in 1995"
TL;DR: In this article, the authors review the theoretical formulation of supersymmetric quantum mechanics and discuss many applications, including shape invariance and operator transformations, and show that a supersymmetry inspired WKB approximation is exact for a class of shape invariant potentials.
2,688 citations
TL;DR: In this article, the authors discuss non-abelian SU(Nc) gauge theory coupled to an adjoint chiral superfield X and a number of fundamental superfields Q, and show that turning on a superpotential W(X) = TrΣl=1k glXl+1 leads to non-trivial long distance dynamics, a large number of multicritical IR fixed points and vacua connected to each other by varying the coefficients gl.
311 citations
TL;DR: In this article, it is shown that the effective space-time superpotential must vanish because there is no place where it can have a pole, and that the world-sheet instanton sum does not see the singularities of the gauge bundle.
238 citations
TL;DR: In this paper, the authors studied the space of perturbations of a pair of dual supersymmetric theories based on an SU(N_c)$ gauge theory with an adjoint $X$ and fundamentals with a superpotential which is polynomial in $X$.
Abstract: We study in detail the space of perturbations of a pair of dual $N=1$ supersymmetric theories based on an $SU(N_c)$ gauge theory with an adjoint $X$ and fundamentals with a superpotential which is polynomial in $X$. The equivalence between them depends on non-trivial facts about polynomial equations, i.e.\ singularity theory. The classical chiral rings of the two theories are different. Quantum mechanically there are new relations in the chiral rings which ensure their equivalence. Duality interchanges ``trivial'' classical relations in one theory with quantum relations in the other and vice versa. We also speculate about the behavior of the theory without the superpotential.
163 citations
TL;DR: In this paper, the authors investigated boundary integrable models that possess N = 2 supersymmetry on the half-space and found that supersymmetric models largely determine boundary action in terms of the bulk, and in particular, the boundary bosonic potential is |W|2, where W is the bulk superpotential.
160 citations
TL;DR: The gauge hierarchy achieved by a fine-tuning in the superpotential would be violated in general due to the nonuniversal SUSY-breaking terms, but it is preserved for a certain class of the soft terms derived from a [ital hidden] ansatz.
Abstract: Supersymmetric grand unified theories with nonuniversal soft supersymmetry- (SUSY-) breaking terms are studied. By integrating out the superheavy fields at a unification scale, we compute their low-energy effective Lagrangian. We find new contributions to the scalar potential specific to the nonuniversal supersymmetry breaking. A D-term contribution to the scalar masses is one example. The gauge hierarchy achieved by a fine-tuning in the superpotential would be violated in general due to the nonuniversal SUSY-breaking terms. We show, however, it is preserved for a certain class of the soft terms derived from a hidden ansatz. We also discuss some phenomenological implications of the nonuniversal supersymmetry breaking, including predictions of the radiative electroweak symmetry-breaking scenario and of no-scale-type models.
144 citations
TL;DR: This work investigates supersymmetric models where neither {ital R} parity nor lepton number is imposed, and finds that neutrino masses can be kept highly suppressed compared to the electroweak scale if the {mu} terms in the superpotential are aligned with the SUSY-breaking bilinear {ital B} terms.
Abstract: We investigate supersymmetric models where neither {ital R} parity nor lepton number is imposed. Neutrino masses can be kept highly suppressed compared to the electroweak scale if the {mu} terms in the superpotential are aligned with the SUSY-breaking bilinear {ital B} terms. This situation arises naturally in the framework of horizontal symmetries. The same symmetries suppress the trilinear {ital R}-parity-violating terms in the superpotential to an acceptable level.
139 citations
TL;DR: In this paper, the authors explore the use of real fermionization as a test case for understanding how specific features of phenomenological interest in the low-energy effective superpotential are realized in exact solutions to heterotic superstring theory.
110 citations
TL;DR: In this paper, the authors discuss supersymmetric SU (2) gauge theory with a single matter field in the I = 3 2 representation, which has a moduli space of exactly degenerate vacua.
106 citations
TL;DR: In this article, a quantum stringy test and a confirmation of a recent proposal of Strominger on the fate of the conifold singularity were presented. But they did not consider string loop corrections to the superpotential of Type II strings.
102 citations
TL;DR: In this paper, the integrable structure of the topological CP1 model is described in terms of a matrix integral which was introduced in a previous article, and the results agree with those predicted by the matrix model.
Abstract: In this paper we describe in some detail the representation of the topological CP1 model in terms of a matrix integral which we have introduced in a previous article. We first discuss the integrable structure of the CP1 model and show that it is governed by an extension of the one-dimensional Toda hierarchy. We then introduce a matrix model which reproduces the sum over holomorphic maps from arbitrary Riemann surfaces onto CP1. We compute intersection numbers on the moduli space of curves using a geometrical method and show that the results agree with those predicted by the matrix model. We also develop a Landau-Ginzburg (LG) description of the CP1 model using a superpotential eX + et0,Q e-X given by the Lax operator of the Toda hierarchy (X is the LG field and t0,Q is the coupling constant of the Kahler class). The form of the superpotential indicates the close connection between CP1 and N=2 supersymmetric sine-Gordon theory which was noted sometime ago by several authors. We also discuss possible generalizations of our construction to other manifolds and present an LG formulation of the topological CP2 model.
TL;DR: The possibility that both the baryon asymmetry and dark matter arise from the late decay of a population of supersymmetric particles is considered in this article, where the decay takes place below the LSP freeze out temperature, a nonthermal distribution of LSPs results with conserved R parity.
TL;DR: In this article, the authors explore the use of real fermionization as a test case for understanding how specific features of phenomenological interest in the low-energy effective superpotential are realized in exact solutions to heterotic superstring theory.
Abstract: We explore the use of real fermionization as a test case for understanding how specific features of phenomenological interest in the low-energy effective superpotential are realized in exact solutions to heterotic superstring theory. We present pedagogic examples of models which realize SO(10) as a level two current algebra on the world-sheet, and discuss in general how higher level current algebras can be realized in the tensor product of simple constituent conformal field theories. We describe formal developments necessary to compute couplings in models built using real fermionization. This allows us to isolate cases of spin structures where the standard prescription for real fermionization may break down.
TL;DR: In this paper, it was shown that the spontaneous breaking of supersymmetry and the gauged R-symmetry can only be handled in local and not in global supersymmetric setting.
Abstract: We discuss local \R-symmetry as a potentially powerful new model building tool. We first review and clarify that a $U(1)$ \R-symmetry can only be gauged in local and not in global supersymmetry. We determine the anomaly-cancellation conditions for the gauged \R-symmetry. For the standard superpotential these equations have {\it no} solution, independently of how many Standard Model singlets are added to the model. There is also no solution when we increase the number of families and the number of pairs of Higgs doublets. When the Green-Schwarz mechanism is employed to cancel the anomalies, solutions only exist for a large number of singlets. We find many anomaly-free family-independent models with an extra $SU(3)_c$ octet chiral superfield. We consider in detail the conditions for an anomaly-free {\it family dependent} $ U(1)_R$ and find solutions with one, two, three and four extra singlets. Only with three and four extra singlets do we naturally obtain sfermion masses of order the weak-scale. For these solutions we consider the spontaneous breaking of supersymmetry and the $R$-symmetry in the context of local supersymmetry. In general the $U(1)_R$ gauge group is broken at or close to the Planck scale. We consider the effects of the \R-symmetry on baryon- and lepton-number violation in supersymmetry. There is no logical connection between a conserved \R-symmetry and conserved \R-parity. For conserved \R-symmetry we have models for all possibilities of conserved or broken \R-parity. Most models predict dominant effects which could be observed at HERA.
TL;DR: In this article, the authors consider the first order contribution of instantons to the mass matrix of a Calabi-Yau manifold with (2,2) world-sheet supersymmetry.
TL;DR: In this article, a model of localization based on the Witten Hamiltonian of supersymmetric quantum mechanics is considered, and the case where the superpotential φ( x ) is a random telegraph process is solved exactly.
TL;DR: In this article, the authors investigated baryogenesis from the coherent production of a scalar condensate along a flat direction of the supersymmetric extension of the standard model (Affleck-Dine mechanism).
Abstract: Baryogenesis from the coherent production of a scalar condensate along a flat direction of the supersymmetric extension of the standard model (Affleck-Dine mechanism) is investigated. Two important effects are emphasized. First, nonrenormalizable terms in the superpotential can lift standard model flat directions at large field values. Second, the finite energy density in the early universe induces soft potentials with curvature of order the Hubble constant. Both these have important implications for baryogenesis, which requires large squark or slepton expectation values to develop along flat directions. In particular, the induced mass squared must be negative. The resulting baryon to entropy ratio is very insensitive to the details of the couplings and initial conditions, but depends on the dimension of the nonrenormalizable operator in the superpotential which stabilizes the flat direction and the reheat temperature after inflation. Unlike the original scenario, an acceptable baryon asymmetry can result without subsequent entropy releases. In the simplest scenario the baryon asymmetry is generated along the $LH_u$ flat direction, and is related to the mass of the lightest neutrino.
TL;DR: In this paper, the exact nonperturbative superpotential of one string theory is given in terms of tree level computations in the other string theory, and concrete examples which provide the stringy realization of the results of Seiberg and Witten on N=2 Yang-Mills theory, corrected by gravitational/stringy effects.
Abstract: We search for $N=2$, $d=4$ theories which can be realized both as heterotic string compactifications on $K_{3}\times T^{2}$ and as type II string compactifications on Calabi-Yau threefolds. In such cases, the exact non-perturbative superpotential of one string theory is given in terms of tree level computations in the other string theory. In particular we find concrete examples which provide the stringy realization of the results of Seiberg and Witten on N=2 Yang-Mills theory, corrected by gravitational/stringy effects. We also discuss some examples which shed light on how the moduli spaces of different N=2 heterotic vacua are connected.
TL;DR: In this paper, the first order contribution of instantons to the mass matrix of these particles is examined and the general conditions under which these couplings vanish classically. But the contribution of individual instantons is not always zero.
Abstract: We consider the gauge neutral matter in the low--energy effective action for string theory compactification on a \cym\ with $(2,2)$ world--sheet supersymmetry. At the classical level these states (the \sing's of $E_6$) correspond to the cohomology group $H^1(\M,{\rm End}\>T)$. We examine the first order contribution of instantons to the mass matrix of these particles. In principle, these corrections depend on the \K\ parameters $t_i$ through factors of the form $e^{2\p i t_i}$ and also depend on the complex structure parameters. For simplicity we consider in greatest detail the quintic threefold $\cp4[5]$. It follows on general grounds that the total mass is often, and perhaps always, zero. The contribution of individual instantons is however nonzero and the contribution of a given instanton may develop poles associated with instantons coalescing for certain values of the complex structure. This can happen when the underlying \cym\ is smooth. Hence these poles must cancel between the coalescing instantons in order that the superpotential be finite. We examine also the \Y\ couplings involving neutral matter \ysing\ and neutral and charged fields \ymix, which have been little investigated even though they are of phenomenological interest. We study the general conditions under which these couplings vanish classically. We also calculate the first--order world--sheet instanton correction to these couplings and argue that these also vanish.
TL;DR: In this article, duality and mirror symmetry properties of Landau-Ginzburg orbifolds were discussed considering their elliptic genera under the duality transform performed by orbifoldizing the LG model via some discrete group of superpotential, and the roles of the untwisted and twisted sectors are exchanged.
Abstract: We discuss duality and mirror symmetry phenomena of Landau-Ginzburg orbifolds considering their elliptic genera Under the duality (or mirror) transform performed by orbifoldizing the Landau-Ginzburg model via some discrete group of the superpotential we observe that the roles of the untwisted and twisted sectors are exchanged As explicit evidence detailed orbifold data are presented for $N=2$ minimal models, Arnold's exceptional singularities, $K3$ surfaces constructed from Arnold's singularities and Fermat hypersurfaces (To appear in the proceedings of the workshop, ``Quantum Field Theory, Integrable Models and Beyond'', Yukawa Institute for Theoretical Physics, Kyoto University, 14-18 February 1994)
TL;DR: In this paper, the authors point out the possibility of spontaneous and hard {ital CP} violation in the scalar potential of the {ital R}-parity broken supersymmetric standard model.
Abstract: We point out the possibility of spontaneous and hard {ital CP} violation in the scalar potential of the {ital R}-parity broken supersymmetric standard model. The existence of spontaneous {ital CP} violation depends crucially on the {ital R}-parity-breaking terms in the superpotential and, in addition, on the choice of the soft supersymmetry-breaking terms. Unlike in theories with {ital R}-parity conservation, it is natural, in the context of the present model, for the sneutrinos to acquire (complex) vacuum expectation values. In the context of this model we examine here the global implications, such as the strength of the {ital CP}-violating interactions and the neutrino masses.
TL;DR: In this article, an extension of the recently proposed dynamical model for the breaking of SU(5)GUT gauge symmetry is presented, in which a pair of massless chiral supermultiplets for Higgs doublets are naturally obtained.
Abstract: We construct an extension of the recently proposed dynamical model for the breaking of SU(5)GUT gauge symmetry, in which a pair of massless chiral supermultiplets for Higgs doublets are naturally obtained. We point out that a model at a specific point in the parameter space of superpotential is regarded as a low-energy effective theory of an supersymmetric gauge model for the strongly interacting hypercolor sector.
TL;DR: In this article, the authors generalize this result to the affine-metric theory of gravity in case of general connections and arbitrary Lagrangian densities invariant under general covariant transformations.
Abstract: In case of the Einstein's gravitation theory and its first order Palatini reformulation, the stress-energy-momentum of gravity has been proved to reduce to the Komar superpotential. We generalize this result to the affine-metric theory of gravity in case of general connections and arbitrary Lagrangian densities invariant under general covariant transformations. In this case, the stress-energy-momentum of gravity comes to the generalized Komar superpotential depending on a Lagrangian density in a precise way.
TL;DR: In this article, a catalog of flat directions of the renormalizable and supersymmetry-preserving part of the scalar potential of the minimal supersymmetric standard model (MSSM) is provided.
Abstract: The scalar potential of the Minimal Supersymmetric Standard Model (MSSM) is nearly flat along many directions in field space. We provide a catalog of the flat directions of the renormalizable and supersymmetry-preserving part of the scalar potential of the MSSM, using the correspondence between flat directions and gauge-invariant polynomials of chiral superfields. We then study how these flat directions are lifted by non-renormalizable terms in the superpotential, with special attention given to the subtleties associated with the family index structure. Several flat directions are lifted only by supersymmetry-breaking effects and by supersymmetric terms in the scalar potential of surprisingly high dimensionality.
TL;DR: In this article, a quantum stringy test and a confirmation of a recent proposal of Strominger on the fate of the conifold singularity were presented. And they also proposed a connection between the spectrum of Bogomolnyi saturated solitons and one-loop string partition function of $N=2$ topological strings.
Abstract: By studying string loop corrections to superpotential of type II strings compactified on Calabi-Yau threefolds we find a quantum stringy test and a confirmation of a recent proposal of Strominger on the fate of the conifold singularity. We also propose a connection between the spectrum of Bogomolnyi saturated solitons and one-loop string partition function of $N=2$ topological strings.
TL;DR: In this paper, the authors derived the exact superpotential in 4d, N = 1 supersymmetric SU(2) theories with triplets and doublets of matter superfields, and the equations of motion can be reorganized into the singularity conditions of an elliptic curve.
Abstract: We derive the exact effective superpotential in 4d, N=1 supersymmetric SU(2) gauge theories with $N_A$ triplets and $2N_f$ doublets of matter superfields. We find the quantum vacua of these theories; the equations of motion (for $N_A=1$) can be reorganized into the singularity conditions of an elliptic curve. From the phase transition points to the Coulomb branch, we find the exact Abelian gauge couplings, $\tau$, for arbitrary bare masses and Yukawa couplings. We thus {\em derive} the result that $\tau$ is a section of an $SL(2,\Z)$ bundle over the moduli space and over the parameters space of bare masses and Yukawa couplings. For $N_c>2$, we derive the exact effective superpotential in branches of supersymmetric $SU(N_c)$ gauge theories with one supermultiplet in the adjoint representation ($N_A=1$) and zero or one flavor ($N_f=0,1$). We find the quantum vacua of these theories; the equations of motion can be reorganized into the singularity conditions of a genus $N_c-1$ hyperelliptic curve. Finally, we present the effective superpotential in the $N_A$, $N_f
TL;DR: In this article, it was shown that anisotropic spin chains of XY type arise by matrix representation of the fermionic terms of hamiltonians of quantum systems whose supersymmetry involves in general no more than a single hermitian supercharge.
TL;DR: In this article, the authors discuss non-abelian gauge theory coupled to an adjoint chiral superfield and a number of fundamental superfields, and show that turning on a superpotential leads to non-trivial long distance dynamics, a large number of multicritical IR fixed points and vacua, connected to each other by varying the coefficients.
Abstract: We discuss non-abelian $SU(N_c)$ gauge theory coupled to an adjoint chiral superfield $X$, and a number of fundamental chiral superfields $Q^i$. Using duality, we show that turning on a superpotential $W(X)=\Tr\sum_{l=1}^k g_l X^{l+1}$ leads to non-trivial long distance dynamics, a large number of multicritical IR fixed points and vacua, connected to each other by varying the coefficients $g_l$.
TL;DR: In this article, the integrable structure of the topological $CP^1$ model is discussed and a matrix model which reproduces the sum over holomorphic maps from arbitrary Riemann surfaces onto $CP$ is introduced.
Abstract: In this paper we describe in some detail the representation of the topological $CP^1$ model in terms of a matrix integral which we have introduced in a previous article. We first discuss the integrable structure of the $CP^1$ model and show that it is governed by an extension of the 1-dimensional Toda hierarchy. We then introduce a matrix model which reproduces the sum over holomorphic maps from arbitrary Riemann surfaces onto $CP^1$. We compute intersection numbers on the moduli space of curves using geometrical method and show that the results agree with those predicted by the matrix model. We also develop a Landau-Ginzburg (LG) description of the $CP^1$ model using a superpotential $e^X+e^{t_{0,Q}}e^{-X}$ given by the Lax operator of the Toda hierarchy ($X$ is the LG field and $t_{0,Q}$ is the coupling constant of the Kahler class). The form of the superpotential indicates the close connection between $CP^1$ and $N=2$ supersymmetric sine-Gordon theory which was noted some time ago by several authors. We also discuss possible generalizations of our construction to other manifolds and present a LG formulation of the topological $CP^2$ model.
TL;DR: In this article, it is shown that the effective space-time superpotential must vanish because there is no place where it can have a pole, and that the world-sheet instanton sum does not see the singularities of the gauge bundle and hence cannot have an analogous pole.
Abstract: It is argued that many linear (0,2) models flow in the infrared to conformally invariant solutions of string theory. The strategy in the argument is to show that the effective space-time superpotential must vanish because there is no place where it can have a pole. This conclusion comes from either of two different analyses, in which the Kahler class or the complex structure of the gauge bundle is varied, while keeping everything else fixed. In the former case, we recover from the linear sigma model the usual simple pole in the ${\bf \bar {27}}^3$ Yukawa coupling but show that an analogous pole does not arise in the couplings of gauge singlet modes. In the latter case, a dimension count shows that the world-sheet instanton sum does not ``see'' the singularities of the gauge bundle and hence cannot have a pole.