Showing papers on "Superpotential published in 1999"
TL;DR: In this paper, it was shown that the Wilson loop observable of a simple knot on S^3 (for any representation) agrees to all orders in N with the corresponding quantity on the topological string side.
Abstract: We find further evidence for the conjecture relating large N Chern-Simons theory on S^3 with topological string on the resolved conifold geometry by showing that the Wilson loop observable of a simple knot on S^3 (for any representation) agrees to all orders in N with the corresponding quantity on the topological string side. For a general knot, we find a reformulation of the knot invariant in terms of new integral invariants, which capture the spectrum (and spin) of M2 branes ending on M5 branes embedded in the resolved conifold geometry. We also find an intriguing link between knot invariants and superpotential terms generated by worldsheet instantons in N=1 supersymmetric theories in 4 dimensions.
492 citations
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TL;DR: In this paper, the authors investigated nonperturbative effects in M-theory compactifications arising from wrapped membranes, and showed that membranes wrapped on rigid supersymmetric 3-cycles induce nonzero corrections to the superpotential.
Abstract: We investigate nonperturbative effects in M-theory compactifications arising from wrapped membranes. In particular, we show that in $d=4, \mathcal{N}=1$ compactifications along manifolds of $G_2$ holonomy, membranes wrapped on rigid supersymmetric 3-cycles induce nonzero corrections to the superpotential. Thus, membrane instantons destabilize many M-theory compactifications. Our computation shows that the low energy description of membrane physics is usefully described in terms of three-dimensional topological field theories, and the superpotential is expressed in terms of topological invariants of the 3-cycle. We discuss briefly some applications of these results. For example, using mirror symmetry we derive a counting formula for supersymmetric three-cycles in certain Calabi-Yau manifolds.
266 citations
TL;DR: In this article, the authors examined supersymmetric SU(N) gauge theories on R 3 × S 1 with a circle of circumference β and derived the superpotential of these theories.
228 citations
TL;DR: In this paper, the Fayet-Iliopoulos conjecture of possible equivalence between the string scale M S and the minimal supersymmetric standard model unification scale M U ≈ 2.5×10 16 GeV is considered in the context of string models.
179 citations
TL;DR: In this article, an exact superpotential for the SU(N) theory on 3 × S1 is derived for the = 1 theories which arise as massive deformations of = 4 supersymmetric Yang-Mills (SYM) theory.
Abstract: An exact superpotential is derived for the = 1 theories which arise as massive deformations of = 4 supersymmetric Yang-Mills (SYM) theory. The superpotential of the SU(N) theory formulated on 3 × S1 is shown to coincide with the complexified potential of the N-body elliptic Calogero-Moser hamiltonian. This superpotential reproduces the vacuum structure predicted by Donagi and Witten for the corresponding four-dimensional theory and also transforms covariantly under the S-duality group of = 4 SYM. The analysis yields exact formulae with interesting modular properties for the condensates of gauge-invariant chiral operators in the four-dimensional theory.
151 citations
TL;DR: In this article, the authors geometrically engineer d=4 N = 1 supersymmetric Yang-Mills theories by considering M theory on various Joyce orbifolds and argue that the superpotential of these models is generated by fractional membrane instantons.
Abstract: We geometrically engineer d=4 N=1 supersymmetric Yang-Mills theories by considering M theory on various Joyce orbifolds. We argue that the superpotential of these models is generated by fractional membrane instantons. The relation of this superpotential to membrane anomalies is also discussed.
142 citations
TL;DR: In this paper, the Wess-Zumino model with quartic superpotential admits stable static solutions in which three domain walls intersect at a junction and shows that configurations saturating it preserve supersymmetry.
Abstract: We argue that the Wess-Zumino model with quartic superpotential admits stable static solutions in which three domain walls intersect at a junction. We derive an energy bound for such junctions and show that configurations saturating it preserve $\frac{1}{4}$ supersymmetry.
138 citations
TL;DR: In this paper, a planar invariant planar dynamics of a superparticle near the horizon of a large mass extreme black hole is described by an O(1, 1, 2)-invariant superconformal mechanics, with the O(2, 2) charge being the orbital angular momentum.
Abstract: The $OSp(2|2)$-invariant planar dynamics of a $D=4$ superparticle near the horizon of a large mass extreme black hole is described by an $N=2$ superconformal mechanics, with the $\mathrm{SO}(2)$ charge being the superparticle's angular momentum. The non-manifest superconformal invariance of the superpotential term is shown to lead to a shift in the $\mathrm{SO}(2)$ charge by the value of its coefficient, which we identify as the orbital angular momentum. The full $SU(1,1|2)$ invariant dynamics is found from an extension to $N=4$ superconformal mechanics.
127 citations
TL;DR: In this paper, a new minimal extension of the minimal supersymmetric standard model (MSSM) by promoting the μ-parameter to a singlet superfield is presented.
126 citations
TL;DR: In this paper, the issue of the soliton mass in two-dimensional models with N = 1$ supersymmetry was reexamine, and it was shown that the property of BPS saturation, i.e. the equality of the Soliton mass to the central charge, remains intact at the quantum level in all orders of the weak coupling expansion.
Abstract: We reexamine the issue of the soliton mass in two-dimensional models with $\mathcal{N}=1$ supersymmetry. The superalgebra has a central extension, and at the classical level the soliton solution preserves 1/2 of supersymmetry which is equivalent to BPS saturation. We prove that the property of BPS saturation, i.e. the equality of the soliton mass to the central charge, remains intact at the quantum level in all orders of the weak coupling expansion. Our key finding is an anomaly in the expression for the central charge. The classical central charge, equal to the jump of the superpotential, is amended by an anomalous term proportional to the second derivative of the superpotential. The anomaly is established by various methods in explicit one-loop calculations. We argue that this one-loop result is not affected by higher orders. We discuss in detail how the impact of the boundary conditions can be untangled from the soliton mass calculation. In particular, the soliton profile and the energy distribution are found at one loop. A ``supersymmetry'' in the soliton mass calculations in the non-supersymmetric models is observed.
111 citations
TL;DR: In this paper, an exact superpotential for the SU(N) theory is derived for the N=1 theories which arise as massive deformations of N=4 supersymmetric Yang-Mills (SYM) theory.
Abstract: An exact superpotential is derived for the N=1 theories which arise as massive deformations of N=4 supersymmetric Yang-Mills (SYM) theory. The superpotential of the SU(N) theory formulated on R^{3}\times S^{1} is shown to coincide with the complexified potential of the N-body elliptic Calogero-Moser Hamiltonian. This superpotential reproduces the vacuum structure predicted by Donagi and Witten for the corresponding four-dimensional theory and also transforms covariantly under the S-duality group of N=4 SYM. The analysis yields exact formulae with interesting modular properties for the condensates of gauge-invariant chiral operators in the four-dimensional theory.
TL;DR: In this paper, the authors consider F/M/Type IIA theory compactified to four, three, or two dimensions on a Calabi-Yau fourfold, and study the behavior near an isolated singularity in the presence of appropriate fluxes and branes.
Abstract: We consider F/M/Type IIA theory compactified to four, three, or two dimensions on a Calabi-Yau four-fold, and study the behavior near an isolated singularity in the presence of appropriate fluxes and branes. We analyze the vacuum and soliton structure of these models, and show that near an isolated singularity, one often generates massless chiral superfields and a superpotential, and in many instances in two or three dimensions one obtains nontrivial superconformal field theories. In the case of two dimensions, we identify some of these theories with certain Kazama-Suzuki coset models, such as the N=2 minimal models.
TL;DR: In this article, a three generation N=1 supersymmetric SU(4)xSU(2)LxSU (2)R model supplemented by an SU(8) hidden gauge symmetry and five Abelian factors is constructed.
Abstract: In the context of the free-fermionic formulation of the heterotic superstring, we construct a three generation N=1 supersymmetric SU(4)xSU(2)LxSU(2)R model supplemented by an SU(8) hidden gauge symmetry and five Abelian factors. The symmetry breaking to the standard model is achieved using vacuum expectation values of a Higgs pair in (4bar,2R)+(4,2R) at a high scale. One linear combination of the Abelian symmetries is anomalous and is broken by vacuum expectation values of singlet fields along the flat directions of the superpotential. All consistent string vacua of the model are completely classified by solving the corresponding system of F- and D-flatness equations including non-renormalizable terms up to sixth order. The requirement of existence of electroweak massless doublets further restricts the phenomenologically viable vacua. The third generation fermions receive masses from the tree-level superpotential. Further, a complete calculation of all non-renormalizable fermion mass terms up to fifth order shows that in certain string vacua the hierarchy of the fermion families is naturally obtained in the model as the second and third generation fermions earn their mass from fourth and fifth order terms. Along certain flat directions it is shown that the ratio of the SU(4) breaking scale and the reduced Planck mass is equal to the up quark ratio m_c/m_t at the string scale. An additional prediction of the model, is the existence of a U(1) symmetry carried by the fields of the hidden sector, ensuring thus the stability of the lightest hidden state. It is proposed that the hidden states may account for the invisible matter of the universe.
TL;DR: In this paper, the authors study Type I string theory compactified on a T 6 / Z 3 orientifold and show that a sector of the theory, which corresponds to placing an odd number of D3-branes at orientifolds fixed points, can give rise to an SU (5) gauge theory with three generations of chiral matter fields.
TL;DR: In this paper, a three-generation N = 1 supersymmetric SU(4) × SU(2)L × SU (2)R model supplemented by an SU(8) hidden gauge symmetry and five Abelian factors is constructed.
TL;DR: In this paper, the authors investigated the physics implications of the class of {ital D}- and {ital F}-flat directions formed from non-Abelian singlets which are proved flat to all orders in the non-renormalizable superpotential, for a prototype quasi-realistic free fermionic string model.
Abstract: From the {open_quotes}top-down{close_quotes} approach we investigate physics implications of the class of {ital D}- and {ital F}-flat directions formed from non-Abelian singlets which are proved flat to all orders in the nonrenormalizable superpotential, for a prototype quasi-realistic free fermionic string model with the standard model gauge group and three families (CHL5). These flat directions have at least an additional U(1){sup {prime}} unbroken at the string scale. For each flat direction, the complete set of effective mass terms and effective trilinear superpotential terms in the observable sector are computed to all orders in the VEV{close_quote}s of the fields in the flat direction. The {open_quotes}string selection rules{close_quotes} disallow a large number of couplings allowed by gauge invariance, resulting in a massless spectrum with a large number of exotics, in most cases excluded by experiment, thus signifying a generic flaw of these models. Nevertheless, the resulting trilinear couplings of the massless spectrum possess a number of interesting features which we analyze for two representative flat directions: for the fermion texture, baryon- and lepton-number violating couplings, {ital R}-parity breaking, non-canonical {mu} terms, and the possibility of electroweak and intermediate scale symmetry breaking scenarios for U(1){sup {prime}}. The gauge coupling predictions are obtained in themore » electroweak scale case. Fermion masses possess t-b and {tau}-{mu} universality, with the string scale Yukawa couplings {ital g} and g/{radical} (2) , respectively. Fermion textures are present for certain flat directions, but only in the down-quark sector. Baryon- and lepton-number violating couplings can trigger proton decay, N-{bar N} oscillations, leptoquark interactions and {ital R}-parity violation, leading to the absence of a stable LSP. {copyright} {ital 1999} {ital The American Physical Society}« less
TL;DR: In this paper, the authors studied supersymmetry breaking via gaugino condensation in vacua of heterotic M-theory with five-branes and determined the form of the low energy matter field Kahler potential.
Abstract: Supersymmetry breaking via gaugino condensation is studied in vacua of heterotic M-theory with five-branes. We show that supersymmetry is still broken by a global mechanism and that the non--perturbative superpotential takes the standard form. When expressed in terms of low energy fields, a modification arises due to a threshold correction in the gauge kinetic function that depends on five--brane moduli. We also determine the form of the low energy matter field Kahler potential. These results are used to discuss the soft supersymmetry breaking parameters, in particular the question of universality.
TL;DR: In this article, a model of interactions of D -dimensional hypermultiplets and supersymmetric gauge multiplets with N = 8 supercharges (D ⩽ 6) can be formulated in the framework of harmonic superspaces.
TL;DR: In this article, a set of distinct flat directions of vacuum expectation values (VEVs) of non-Abelian singlet fields that all produce solely the MSSM spectrum is studied.
Abstract: Recently, we demonstrated the existence of heterotic--string solutions in which the observable sector effective field theory just below the string scale reduces to that of the MSSM, with the standard observable gauge group being just SU(3)_C x SU(2)_L x U(1)_Y and the SU(3)_C x SU(2)_L x U(1)_Y-charged spectrum of the observable sector consisting solely of the MSSM spectrum. Associated with this model is a set of distinct flat directions of vacuum expectation values (VEVs) of non-Abelian singlet fields that all produce solely the MSSM spectrum. In this paper, we study the effective superpotential induced by these choices of flat directions. We investigate whether sufficient degrees of freedom exist in these singlet flat directions to satisfy various phenomenological constraints imposed by the observed Standard Model data. For each flat direction, the effective superpotential is given to sixth order. The variations in the singlet and hidden sector low energy spectrums are analyzed. We then determine the mass matrices (to all finite orders) for the three generations of MSSM quarks and leptons. Possible Higgs mu-terms are investigated. We conclude by considering generalizations of our flat directions involving VEVs of non-Abelian fields.
TL;DR: In this article, a new Hamiltonian inspired covariant formula is proposed to define the superponential and the physical charges associated to a gauge symmetry. But no associated central charge is found for n ⩾ 2.
TL;DR: In this paper, the authors investigate F and D-flat directions in several three-generation SU(3)CSU(2)LU (1)Y free-fermionic string models and discuss the typical scenarios that generically arise.
TL;DR: In this paper, the Lagrangian formulation of general relativity for perturbations with respect to a background spacetime is considered and the superpotential is obtained by combining Noether's method with Belinfante's "symmetrization'' procedure.
Abstract: We first consider the Lagrangian formulation of general relativity for perturbations with respect to a background spacetime. We show that by combining Noether's method with Belinfante's "symmetrization'' procedure we obtain conserved vectors that are independent of any divergence added to the perturbed Hilbert Lagrangian. We also show that the corresponding perturbed energy- momentum tensor is symmetrical and divergenceless but only on backgrounds that are "Einstein spaces" in the sense of A.Z. Petrov. de Sitter or anti-de Sitter and Einstein "spacetimes" are Einstein spaces but in general Friedmann-Robertson -Walker spacetimes are not. Each conserved vector is a divergence of an anti- symmetric tensor, a "superpotential". We find superpotentials which are a generalization of Papapetrou's superpotential and are rigorously linear, even for large perturbations, in terms of the inverse metric density components and their first order derivatives. The superpotentials give correct globally conserved quantities at spatial infinity. They resemble Abbott and Deser's superpotential, but give correctly the Bondi-Sachs total four-momentum at null infinity. Next we calculate conserved vectors and superpotentials for perturbations of a Friedmann-Robertson-Walker background associated with its 15 conformal Killing vectors given in a convenient form. The integral of each conserved vector in a finite volume V at a given conformal time is equal to a surface integral on the boundary of V of the superpotential. For given boundary conditions each such integral is part of a flux whose total through a closed hypersurface is equal to zero. For given boundary conditions on V, the integral can be considered as an "integral constraint" on data in the volume...
TL;DR: In this article, the authors obtained = 1 SU(N)k gauge theories with bifundamental matter and a quartic superpotential as the low energy theory on D3-branes at singular points.
Abstract: We obtain = 1 SU(N)k gauge theories with bifundamental matter and a quartic superpotential as the low energy theory on D3-branes at singular points. These theories generalize that on D3-branes at a conifold point, studied recently by Klebanov and Witten. For k = 3 the defining equation of the singular point is that of an isolated D4 singularity. For k > 3 we obtain a family of multimodular singularities. The considered SU(N)k theories flow in the infrared to a non-trivial fixed point. We analyze the AdS/CFT correspondence for our examples.
TL;DR: In this article, the authors show how to derive the correct superpotential through Lagrangian methods, by applying a criterion proposed recently by one of us, and verify the equivalence with the Hamiltonian formalism.
TL;DR: In this article, the SU(2) supersymmetric Yang-Mills quantum mechanics up to two constants was derived from the F4 term completion of the matrix theory, and the results showed that the stringent constraints from the supersymmetry are responsible for the agreement between matrix theory and supergravity.
TL;DR: In this article, supersymmetric quantum mechanics (SUSY QM) is applied to multidimensional Schrodinger equations involving nonseparable potentials, which result in a system of coupled differential equations.
Abstract: We apply supersymmetric quantum mechanics (SUSY QM) to multidimensional Schrodinger equations involving nonseparable potentials, which result in a system of coupled differential equations, where instead of the conventional definition of a scalar superpotential we introduce a superpotential matrix and succeed in applying SUSY QM to the coupled system. Finally, we discuss the shape-invariance condition for the potential matrix of such a system.
TL;DR: In this article, the implementation of non-Abelian Wilson lines in D=4 N=1 Type IIB orientifold constructions is addressed. And the particle spectrum and the trilinear superpotential are analyzed.
Abstract: We address the implementation of non-Abelian Wilson lines in D=4 N=1 Type IIB orientifold constructions. We present an explicit three-family example with the gauge group (U(4)xU(2)xSU(2)xSU(2))^2x(U(6)xSp(4))^2 and give the particle spectrum and the trilinear superpotential. Emphasizing the new subtleties associated with the introduction of non-Abelian Wilson lines, we show that the Abelian gauge anomalies are cancelled by the Green-Schwarz-type mechanism, and calculate the Fayet-Iliopoulos terms and gauge coupling corrections. The analysis thus sets a stage for further investigations of the phenomenological implications of this model.
TL;DR: In this paper, the authors studied bottom-tau coupling unification in the simplest extension of the Minimal Supersymmetric Standard Model (MSSM) which incorporates R-parity violation through a bilinear superpotential term.
TL;DR: In this paper, the authors examined N = 1 supersymmetric gauge theories which confine in the presence of a tree-level superpotential and showed the confining spectra which satisfy the 't Hooft anomaly matching conditions.
Abstract: We examine N=1 supersymmetric gauge theories which confine in the presence of a tree-level superpotential. We show the confining spectra which satisfy the 't Hooft anomaly matching conditions and give a simple method to find the confining superpotential. Using this method we fix the confining superpotentials in the simplest cases, and show how these superpotentials are generated by multi-instanton effects in the dual theory. These new type of confining theories may be useful for model building, since the size of the matter content is not restricted by an index constraint. Therefore, one expects that a large variety of new confining spectra can be obtained using such models.
TL;DR: In this paper, it was shown that intermediate scales in supersymmetric grand unified theories may exist naturally, due to the violation of the survival principle, which leads to a plethora of light supermultiplets whose masses are generated only by higher dimensional operators and thus suppressed by the cutoff scale.