Showing papers on "Superpotential published in 2007"

Notes on superconformal Chern-Simons-Matter theories

Abstract: The three dimensional = 2 supersymmetric Chern-Simons theory coupled to matter fields, possibly deformed by a superpotential, give rise to a large class of exactly conformal theories with Lagrangian descriptions. These theories can be arbitrarily weakly coupled, and hence can be studied perturbatively. We study the theories in the large N limit, and compute the two-loop anomalous dimension of certain long operators. Our result suggests that various = 2 U(N) Chern-Simons theories coupled to suitable matter fields are dual to open or closed string theories in AdS4, which are not yet constructed.

From ten to four and back again: how to generalize the geometry

Abstract: We discuss the four-dimensional N = 1 effective approach in the study of warped type II flux compactifications with SU(3) × SU(3)-structure to AdS4 or flat Minkowski space-time. The non-trivial warping makes it natural to use a supergravity formulation invariant under local complexified Weyl transformations. We obtain the classical superpotential from a standard argument involving domain walls and generalized calibrations and show how the resulting F-flatness and D-flatness equations exactly reproduce the full ten-dimensional supersymmetry equations. Furthermore, we consider the effect of non-perturbative corrections to this superpotential arising from gaugino condensation or Euclidean D-brane instantons. For the latter we derive the supersymmetry conditions in N = 1 flux vacua in full generality. We find that the non-perturbative corrections induce a quantum deformation of the internal generalized geometry. Smeared instantons allow to understand KKLT-like AdS vacua from a ten-dimensional point of view. On the other hand, non-smeared instantons in IIB warped Calabi-Yau compactifications `destabilize' the Calabi-Yau complex structure into a genuine generalized complex one. This deformation gives a geometrical explanation of the non-trivial superpotential for mobile D3-branes induced by the non-perturbative corrections.

Gaugino Condensates and D-terms from D7-branes

Abstract: We investigate, at the microscopic level, the compatibility between D-term potentials from world-volume fluxes on D7-branes and non-perturbative superpotentials arising from gaugino condensation on a different stack of D7-branes. This is motivated by attempts to construct metastable de Sitter vacua in type IIB string theory via D-term uplifts. We find a condition under which the Kahler modulus, T, of a Calabi-Yau 4-cycle gets charged under the anomalous U(1) on the branes with flux. If in addition this 4-cycle is wrapped by a stack of D7-branes on which gaugino condensation takes place, the question of U(1)-gauge invariance of the (T-dependent) non-perturbative superpotential arises. In this case an index theorem guarantees that strings, stretching between the two stacks, yield additional charged chiral fields which also appear in the superpotential from gaugino condensation. We check that the charges work out to make this superpotential gauge invariant, and we argue that the mechanism survives the inclusion of higher curvature corrections to the D7-brane action.

Stringy instantons and quiver gauge theories

Abstract: We explore contributions to the 4D effective superpotential which arise from Euclidean D3 branes (''instantons'') that intersect space-filling D-branes These effects can perturb the effective field theory on the space-filling branes by nontrivial operators composed of charged matter fields, changing the vacuum structure in a qualitative way in some examples Our considerations are exemplified throughout by a careful study of a fractional brane configuration on a del Pezzo surface

Instanton Induced Neutrino Majorana Masses in CFT Orientifolds with MSSM-like spectra

Abstract: Recently it has been shown that string instanton effects may give rise to neutrino Majorana masses in certain classes of semi-realistic string compactifications. In this paper we make a systematic search for supersymmetric MSSM-like Type II Gepner orientifold constructions admitting boundary states associated with instantons giving rise to neutrino Majorana masses and other L- and/or B-violating operators. We analyze the zero mode structure of D-brane instantons on general type II orientifold compactifications, and show that only instantons with O(1) symmetry can have just the two zero modes required to contribute to the 4d superpotential. We however discuss how the addition of fluxes and/or possible non-perturbative extensions of the orientifold compactifications would allow

Stringy instantons at orbifold singularities

Abstract: We study the effects produced by D-brane instantons on the holomorphic quantities of a D-brane gauge theory at an orbifold singularity. These effects are not limited to reproducing the well known contributions of the gauge theory instantons but also generate extra terms in the superpotential or the prepotential. On these brane instantons there are some neutral fermionic zero-modes in addition to the ones expected from broken supertranslations. They are crucial in correctly reproducing effects which are dual to gauge theory instantons, but they may make some other interesting contributions vanish. We analyze how orientifold projections can remove these zero-modes and thus allow for new superpotential terms. These terms contribute to the dynamics of the effective gauge theory, for instance in the stabilization of runaway directions.

Computation of D-brane instanton induced superpotential couplings: Majorana masses from string theory

Abstract: We perform a detailed conformal field theory analysis of $D2$-brane instanton effects in four-dimensional type IIA string vacua with intersecting $D6$-branes. In particular, we explicitly compute instanton induced fermion two-point couplings which play the role of perturbatively forbidden Majorana mass terms for right-handed neutrinos or MSSM $\ensuremath{\mu}$ terms. These results can readily be extended to higher-dimensional operators. In concrete realizations of such nonperturbative effects, the Euclidean $D2$-brane has to wrap a rigid, supersymmetric cycle with strong constraints on the zero-mode structure. Their implications for type IIA compactifications on the ${T}^{6}/({\mathbb{Z}}_{2}\ifmmode\times\else\texttimes\fi{}{\mathbb{Z}}_{2})$ orientifold with discrete torsion are analyzed. We also construct a local supersymmetric GUT-like model allowing for a class of Euclidean $D2$-branes whose fermionic zero modes meet all the constraints for generating Majorana masses in the phenomenologically allowed regime. Together with perturbatively realized Dirac masses, these nonperturbative couplings give rise to the seesaw mechanism.

Opening Mirror Symmetry on the Quintic

Abstract: Aided by mirror symmetry, we determine the number of holomorphic disks ending on the real Lagrangian in the quintic threefold. We hypothesize that the tension of the domainwall between the two vacua on the brane, which is the generating function for the open Gromov-Witten invariants, satisfies a certain extension of the Picard-Fuchs differential equation governing periods of the mirror quintic. We verify consistency of the monodromies under analytic continuation of the superpotential over the entire moduli space. We further check the conjecture by reproducing the first few instanton numbers by a localization computation directly in the A-model, and verifying Ooguri-Vafa integrality. This is the first exact result on open string mirror symmetry for a compact Calabi-Yau manifold.

Stringy Instantons at Orbifold Singularities

Abstract: We study the effects produced by D-brane instantons on the holomorphic quantities of a D-brane gauge theory at an orbifold singularity. These effects are not limited to reproducing the well known contributions of the gauge theory instantons but also generate extra terms in the superpotential or the prepotential. On these brane instantons there are some neutral fermionic zero-modes in addition to the ones expected from broken supertranslations. They are crucial in correctly reproducing effects which are dual to gauge theory instantons, but they may make some other interesting contributions vanish. We analyze how orientifold projections can remove these zero-modes and thus allow for new superpotential terms. These terms contribute to the dynamics of the effective gauge theory, for instance in the stabilization of runaway directions.

Dimers and orientifolds

Abstract: We introduce new techniques based on brane tilings to investigate D3-branes probing orientifolds of toric Calabi-Yau singularities. With these new tools, one can write down many orientifold models and derive the resulting low-energy gauge theories living on the D-branes. Using the set of ideas in this paper one recovers essentially all orientifolded theories known so far. Furthermore, new orientifolds of non-orbifold toric singularities are obtained. The possible applications of the tools presented in this paper are diverse. One particular application is the construction of models which feature dynamical supersymmetry breaking as well as the computation of D-instanton induced superpotential terms.

D-brane instantons on the T**6 / Z(3) orientifold

Abstract: We give a detailed microscopic derivation of gauge and stringy instanton generated superpotentials for gauge theories living on D3-branes at Z_3-orientifold singularities. Gauge instantons are generated by D(-1)-branes and lead to Affleck, Dine and Seiberg (ADS) like superpotentials in the effective N=1 gauge theories with three generations of bifundamental and anti/symmetric matter. Stringy instanton effects are generated by Euclidean ED3-branes wrapping four-cycles on T^6/\Z_3. They give rise to Majorana masses in one case and non-renormalizable superpotentials for the other cases. Finally we determine the conditions under which ADS like superpotentials are generated in N=1 gauge theories with adjoints, fundamentals, symmetric and antisymmetric chiral matter.

Lifting D-instanton zero modes by recombination and background fluxes

Abstract: We study the conditions under which D-brane instantons in Type II orientifold compactifications generate a non-perturbative superpotential. If the instanton is non-invariant under the orientifold action, it carries four instead of the two Goldstone fermions required for superpotential contributions. Unless these are lifted, the instanton can at best generate higher fermionic F-terms of Beasley-Witten type. We analyse two strategies to lift the additional zero modes. First we discuss the process of instantonic brane recombination in Type IIA orientifolds. We show that in some cases charge invariance of the measure enforces the presence of further zero modes which, unlike the Goldstinos, cannot be absorbed. In other cases, the instanton exhibits reparameterisation zero modes after recombination and a superpotential is generated if these are lifted by suitable closed or open string couplings. In the second part of the paper we address lifting the extra Goldstinos of D3-brane instantons by supersymmetric three-form background fluxes in Type IIB orientifolds. This requires non-trivial gauge flux on the instanton. Only if the part of the fermionic action linear in the gauge flux survives the orientifold projection can the extra Goldstinos be lifted.

Simple model of direct gauge mediation of metastable supersymmetry breaking

Abstract: We construct a model of direct gauge mediation of metastable supersymmetry breaking by simply deforming the Intriligator, Seiberg, and Shih model in terms of a dual meson superpotential mass term. No extra matter field is introduced. The deformation explicitly breaks a $U(1{)}_{R}$ symmetry and pseudomoduli have a nonzero VEV at one-loop. Our metastable supersymmetry breaking vacuum turns out to be sufficiently long-lived. By gauging a subgroup of flavor symmetry, our model can directly couple to the standard model, which leads to nonvanishing gaugino mass generation. It is also shown that our model can evade the Landau pole problem. We show the parameters in the supersymmetry breaking sector are phenomenologically constrained.

Non-perturbative SQCD Superpotentials from String Instantons

Abstract: The Affleck-Dine-Seiberg instanton generated superpotential for SQCD with Nf = Nc−1 flavours is explicitly derived from a local model of engineered intersecting D6-branes with a single E2-instanton. This computation extends also to symplectic gauge groups with Nf = Nc flavours.

Instanton Induced Neutrino Majorana Masses in CFT Orientifolds with MSSM-like spectra

Abstract: Recently it has been shown that string instanton effects may give rise to neutrino Majorana masses in certain classes of semi-realistic string compactifications. In this paper we make a systematic search for supersymmetric MSSM-like Type II Gepner orientifold constructions admitting boundary states associated with instantons giving rise to neutrino Majorana masses and other L- and/or B-violating operators. We analyze the zero mode structure of D-brane instantons on general type II orientifold compactifications, and show that only instantons with O(1) symmetry can have just the two zero modes required to contribute to the 4d superpotential. We however discuss how the addition of fluxes and/or possible non-perturbative extensions of the orientifold compactifications would allow also instantons with $Sp(2)$ and U(1) symmetries to generate such superpotentials. In the context of Gepner orientifolds with MSSM-like spectra, we find no models with O(1) instantons with just the required zero modes to generate a neutrino mass superpotential. On the other hand we find a number of models in one particular orientifold of the Gepner model $(2,4,22,22)$ with $Sp(2)$ instantons with a few extra uncharged non-chiral zero modes which could be easily lifted by the mentioned effects. A few more orientifold examples are also found under less stringent constraints on the zero modes. This class of $Sp(2)$ instantons have the interesting property that R-parity conservation is automatic and the flavour structure of the neutrino Majorana mass matrices has a simple factorized form.

A SUSY A4 model for fermion masses and mixings

Abstract: We study a supersymmetric extension of the Standard Model based on discrete A4xZ3xZ4 flavor symmetry. We obtain quark mixing angles as well as a realistic fermion mass spectrum and we predict tribimaximal leptonic mixing by a spontaneous breaking of A4. The top quark Yukawa interaction is present at the renormalizable level in the superpotential while all the other Yukawa interactions arise only at higher orders. We study the Higgs potential and show that it can potentially solve the so called vacuum alignment problem. The leading order predictions are not spoiled by subleading corrections.

On F-term contribution to effective action

Abstract: We apply equivariant integration technique, developed in the context of instanton counting, to two dimensional = 2 supersymmetric Yang-Mills models. The expression for the twisted superpotential for U(N) model is conjectured. Connections to the four dimensional case are discussed.

B-type defects in Landau-Ginzburg models

Abstract: We consider Landau-Ginzburg models with possibly different superpotentials glued together along one-dimensional defect lines. Defects preserving B-type supersymmetry can be represented by matrix factorisations of the difference of the superpotentials. The composition of these defects and their action on B-type boundary conditions is described in this framework. The cases of Landau-Ginzburg models with superpotential W = Xd and W = Xd+Z2 are analysed in detail, and the results are compared to the CFT treatment of defects in N = 2 superconformal minimal models to which these Landau-Ginzburg models flow in the IR.

S_4 Flavor Symmetry Embedded into SU(3) and Lepton Masses and Mixing

Abstract: Based on an assumption that an S_4 flavor symmetry is embedded into SU(3), a lepton mass matrix model is investigated. A Frogatt-Nielsen type model is assumed, and the flavor structures of the masses and mixing are caused by VEVs of SU(2)_L-singlet scalars \phi_u and \phi_d which are nonets (8+1) of the SU(3) flavor symmetry, and which are broken into 2+3+3' and 1 of S_4. If we require the invariance under the transformation (\phi^{(8)},\phi^{(1)}) \to (-\phi^{(8)},+\phi^{(1)}) for the superpotential of the nonet field \phi^{(8+1)}, the model leads to a beautiful relation for the charged lepton masses. The observed tribimaximal neutrino mixing is understood by assuming two SU(3) singlet right-handed neutrinos u_R^{(\pm)} and an SU(3) triplet scalar \chi.

Instantons and holomorphic couplings in intersecting D-brane models

Abstract: We clarify certain aspects and discuss extensions of the recently introduced string D-instanton calculus (hep-th/0609191). The one-loop determinants are related to one-loop open string threshold corrections in intersecting D6-brane models. Utilising a non-renormalisation theorem for the holomorphic Wilsonian gauge kinetic functions, we derive a number of constraints for the moduli dependence of the matter field Kahler potentials of intersecting D6-brane models on the torus. Moreover, we compute string one-loop corrections to the Fayet-Iliopoulos terms on the D6-branes finding that they are proportional to the gauge threshold corrections. Employing these results, we discuss the issue of holomorphy for E2-instanton corrections to the superpotential. Eventually, we discuss E2-instanton corrections to the gauge kinetic functions and the FI-terms.

Heterotic vortex strings

Abstract: We determine the low-energy = (0,2) worldsheet dynamics of vortex strings in a large class of non-Abelian = 1 supersymmetric gauge theories.

Instantons and Holomorphic Couplings in Intersecting D-brane Models

Abstract: We clarify certain aspects and discuss extensions of the recently introduced string D-instanton calculus (hep-th/0609191). The one-loop determinants are related to one-loop open string threshold corrections in intersecting D6-brane models. Utilising a non-renormalisation theorem for the holomorphic Wilsonian gauge kinetic functions, we derive a number of constraints for the moduli dependence of the matter field Kaehler potentials of intersecting D6-brane models on the torus. Moreover, we compute string one-loop corrections to the Fayet-Iliopoulos terms on the D6-branes finding that they are proportional to the gauge threshold corrections. Employing these results, we discuss the issue of holomorphy for E2-instanton corrections to the superpotential. Eventually, we discuss E2-instanton corrections to the gauge kinetic functions and the FI-terms.

Non-Perturbative Corrections and Modularity in N=1 Type IIB Compactifications

Abstract: Non-perturbative corrections and modular properties of four-dimensional type IIB Calabi-Yau orientifolds are discussed. It is shown that certain non-perturbative α' corrections survive in the large volume limit of the orientifold and periodically correct the Kahler potential. These corrections depend on the NS-NS two form and have to be completed by D-instanton contributions to transform covariantely under symmetries of the type IIB orientifold background. It is shown that generically also the D-instanton superpotential depends on the two-form moduli as well as on the complex dilaton. These contributions can arise through theta-functions with the dilaton as modular parameter. An orientifold of the Enriques Calabi-Yau allows to illustrate these general considerations. It is shown that this compactification leads to a controlled four-dimensional = 1 effective theory due to the absence of various quantum corrections. Making contact to the underlying topological string theory the D-instanton superpotential is proposed to be related to a specific modular form counting D3, D1, D(-1) degeneracies on the Enriques Calabi-Yau.

Non-perturbative superpotentials across lines of marginal stability

Abstract: We discuss the behaviour of non-perturbative superpotentials in 4d N=1 type II compactifications (and orientifolds thereof) near lines of marginal stability, where the spectrum of contributing BPS D-brane instantons changes discontinuously. The superpotential is nevertheless continuous, in agreement with its holomorphic dependence on the closed string moduli. The microscopic mechanism ensuring this continuity involves novel contributions to the superpotential: As an instanton becomes unstable against decay to several instantons, the latter provide a multi-instanton contribution which reconstructs that of the single-instanton before decay. The process can be understood as a non-perturbative lifting of additional fermion zero modes of an instanton by interactions induced by other instantons. These effects provide mechanisms via which instantons with U(1) symmetry can contribute to the superpotential. We provide explicit examples of these effects for non-gauge D-brane instantons, and for D-brane gauge instantons (where the motions in moduli space can be interpreted as Higgsing, or Seiberg dualities).

Minimal standard heterotic string models

Abstract: Three generation heterotic string vacua in the free fermionic formulation gave rise to models with solely the MSSM states in the observable standard model charged sector. The relation of these models to Z2×Z2 orbifold compactifications dictates that they produce three pairs of untwisted Higgs multiplets. The reduction to one pair relies on the analysis of supersymmetric flat directions, which give a superheavy mass to the dispensable Higgs states. We explore the removal of the extra Higgs representations by using the free fermion boundary conditions, and hence we work directly at the string level, rather than in the effective low energy field theory. We present a general mechanism that achieves this reduction by using asymmetric boundary conditions between the left- and right-moving internal fermions. We incorporate this mechanism in explicit string models containing three twisted generations and a single untwisted Higgs doublet pair. We further demonstrate that an additional effect of the asymmetric boundary conditions is to substantially reduce the supersymmetric moduli space.

A new method for finding vacua in string phenomenology

Abstract: One of the central problems of string-phenomenology is to find stable vacua in the four dimensional effective theories which result from compactification. We present an algorithmic method to find all of the vacua of any given string-phenomenological system in a huge class. In particular, this paper reviews and then extends hep-th/0606122 to include various non-perturbative effects. These include gaugino condensation and instantonic contributions to the superpotential.