Showing papers on "Superpotential published in 2006"
TL;DR: In this paper, the potential governing D3-brane motion in a warped throat region of a string compactification with internal fluxes and wrapped D-branes was studied and a closed-string channel computation of the loop corrections to the nonperturbative superpotential that stabilizes the volume was presented.
Abstract: We study the potential governing D3-brane motion in a warped throat region of a string compactification with internal fluxes and wrapped D-branes. If the Kahler moduli of the compact space are stabilized by nonperturbative effects, a D3-brane experiences a force due to its interaction with D-branes wrapping certain four-cycles. We compute this interaction, as a correction to the warped four-cycle volume, using explicit throat backgrounds in supergravity. This amounts to a closed-string channel computation of the loop corrections to the nonperturbative superpotential that stabilizes the volume. We demonstrate that for warped conical spaces the superpotential correction is given by the embedding equation specifying the wrapped four-cycle, in agreement with the general form proposed by Ganor. We verify that the corrected gauge coupling on wrapped D7-branes is holomorphic. Finally, our results have applications to cosmological inflation models in which the inflaton corresponds to a D3-brane moving in a warped throat.
308 citations
TL;DR: In this article, it was shown that under general conditions there is at least one natural inflationary direction for the Kahler moduli of type-IIB flux compactifications, and that slow-roll inflation then occurs without a fine tuning of parameters, evading the η problem of F-term inflation.
Abstract: We show that under general conditions there is at least one natural inflationary direction for the Kahler moduli of type-IIB flux compactifications. This requires a Calabi-Yau which has h^{1,1}>2$>h2,1>h1,1>2 and for which the structure of the scalar potential is as in the recently found exponentially large volume compactifications. We also need - although these conditions may be relaxed - at least one Kahler modulus whose only non-vanishing triple-intersection is with itself and which appears by itself in the non-perturbative superpotential. Slow-roll inflation then occurs without a fine tuning of parameters, evading the η problem of F-term inflation. In order to obtain COBE-normalised density perturbations, the stabilised volume of the Calabi-Yau must be (105−107) in string units, and the inflationary scale Minfl ~ 1013 GeV. We find a robust model independent prediction for the spectral index of 1−2/Ne = 0.960→0.967, depending on the number of efoldings.
300 citations
TL;DR: In this paper, the authors consider type II string theory in space-time backgrounds which admit eight supercharges, and demonstrate how the corresponding ten-dimensional supergravity theories can in part be rewritten using generalised O(6,6)-covariant fields, in a form that strongly resembles that of four-dimensional N = 2 supergravity, and precisely coincides with such after an appropriate Kaluza-Klein reduction.
Abstract: We consider type II string theory in space-time backgrounds which admit eight supercharges. Such backgrounds are characterized by the existence of a (generically non-integrable) generalized SU(3) × SU(3) structure. We demonstrate how the corresponding ten-dimensional supergravity theories can in part be rewritten using generalised O(6,6)-covariant fields, in a form that strongly resembles that of four-dimensional N = 2 supergravity, and precisely coincides with such after an appropriate Kaluza-Klein reduction. Specifically we demonstrate that the NS sector admits a special Kahler geometry with Kahler potentials given by the Hitchin functionals. Furthermore we explicitly compute the N = 2 version of the superpotential from the transformation law of the gravitinos, and find its N = 1 counterpart.
268 citations
TL;DR: In this article, the authors construct supergravity plus branes solutions, which they argue to be related to 4d SQCD with a quartic superpotential, and support their field theory interpretation by studying a variety of features like $R$-symmetry breaking, instantons, Seiberg duality, Wilson loops and pair creation, running of couplings and domain walls.
Abstract: We construct supergravity plus branes solutions, which we argue to be related to 4d $\mathcal{N}=1$ SQCD with a quartic superpotential. The geometries depend on the ratio ${N}_{f}/{N}_{c}$ which can be kept of order one, present a good singularity at the origin, and are weakly curved elsewhere. We support our field theory interpretation by studying a variety of features like $R$-symmetry breaking, instantons, Seiberg duality, Wilson loops and pair creation, running of couplings, and domain walls. In a second part of this paper, we address a different problem: the analysis of the interesting physics of different members of a family of supergravity solutions dual to (unflavored) $\mathcal{N}=1$ SYM plus some UV completion.
267 citations
TL;DR: In this article, it was shown that invariance under type IIB S-duality requires the introduction of a new set of fluxes leading to further superpotential terms.
Abstract: We generalize the recent proposal that invariance under T-duality leads to additional non-geometric fluxes required so that superpotentials in type IIA and type IIB orientifolds match. We show that invariance under type IIB S-duality requires the introduction of a new set of fluxes leading to further superpotential terms. We find new classes of = 1 supersymmetric Minkowski vacua based on type IIB toroidal orientifolds in which not only dilaton and complex moduli but also K?hler moduli are fixed. The chains of dualities relating type II orientifolds to heterotic and M-theory compactifications suggests the existence of yet further flux degrees of freedom. Restricting to a particular type IIA/IIB or heterotic compactification only some of these degrees of freedom have a simple perturbative and/or geometric interpretation.
196 citations
TL;DR: It is shown that all domain-wall solutions of gravity coupled to scalar fields for which the world-volume geometry is Minkowski or anti-de Sitter admit Killing spinors, and satisfy corresponding first-order equations involving a superpotential determined by the solution.
Abstract: We show that all domain-wall solutions of gravity coupled to scalar fields for which the world-volume geometry is Minkowski or anti-de Sitter admit Killing spinors, and satisfy corresponding first-order equations involving a superpotential determined by the solution. By analytic continuation, all flat or closed Friedmann-Lemaitre-Robertson-Walker cosmologies are shown to satisfy similar first-order equations arising from the existence of 'pseudo Killing' spinors.
190 citations
TL;DR: In this paper, a simple model of supersymmetry breaking with all small mass scales generated dynamically is proposed. But the model is not suitable for general supersymmetric Yang-Mills models.
Abstract: We provide a method for obtaining simple models of supersymmetry breaking, with all small mass scales generated dynamically, and illustrate it with explicit examples. We start from models of perturbative supersymmetry breaking, such as O'Raifeartaigh and Fayet models, that would respect an R symmetry if their small input parameters transformed as the superpotential does. By coupling the system to a pure supersymmetric Yang-Mills theory (or a more general supersymmetric gauge theory with dynamically small vacuum expectation values), these parameters are replaced by powers of its dynamical scale in a way that is naturally enforced by the symmetry. We show that supersymmetry breaking in these models may be straightforwardly mediated to the supersymmetric Standard Model, obtain complete models of direct gauge mediation, and comment on related model building strategies that arise in this simple framework.
173 citations
TL;DR: In this paper, the authors present a new version of the racetrack inflation model, which is based on an explicit compactification of type IIB string theory, and obtain the COBE-normalized spectrum of metric perturbations and an inflationary scale of 3 × 1014 GeV.
Abstract: We present a new version of our racetrack inflation scenario which, unlike our original proposal, is based on an explicit compactification of type IIB string theory: the Calabi-Yau manifold 4[1,1,1,6,9]. The axion-dilaton and all complex structure moduli are stabilized by fluxes. The remaining 2 Kahler moduli are stabilized by a nonperturbative superpotential, which has been explicitly computed. For this model we identify situations for which a linear combination of the axionic parts of the two Kahler moduli acts as an inflaton. As in our previous scenario, inflation begins at a saddle point of the scalar potential and proceeds as an eternal topological inflation. For a certain range of inflationary parameters, we obtain the COBE-normalized spectrum of metric perturbations and an inflationary scale of M = 3 × 1014 GeV. We discuss possible changes of parameters of our model and argue that anthropic considerations favor those parameters that lead to a nearly flat spectrum of inflationary perturbations, which in our case is characterized by the spectral index ns = 0.95.
148 citations
TL;DR: In this paper, it was shown that invariance under type IIB S-duality requires the introduction of a new set of fluxes leading to further superpotential terms.
Abstract: We generalize the recent proposal that invariance under T-duality leads to additional non-geometric fluxes required so that superpotentials in type IIA and type IIB orientifolds match. We show that invariance under type IIB S-duality requires the introduction of a new set of fluxes leading to further superpotential terms. We find new classes of N=1 supersymmetric Minkowski vacua based on type IIB toroidal orientifolds in which not only dilaton and complex moduli but also Kahler moduli are fixed. The chains of dualities relating type II orientifolds to heterotic and M-theory compactifications suggests the existence of yet further flux degrees of freedom. Restricting to a particular type IIA/IIB or heterotic compactification only some of these degrees of freedom have a simple perturbative and/or geometric interpretation.
147 citations
TL;DR: In this paper, a general expression for the flux potential of type II compactifications with D7/D3 branes was derived, including open string moduli and 2-form fluxes on the branes.
144 citations
TL;DR: In this paper, the authors present a new version of the racetrack inflation model, which is based on an explicit compactification of type IIB string theory, and obtain the COBE-normalized spectrum of metric perturbations and an inflationary scale of M = 3 x 10^{14} GeV.
Abstract: We present a new version of our racetrack inflation scenario which, unlike our original proposal, is based on an explicit compactification of type IIB string theory: the Calabi-Yau manifold P^4_[1,1,1,6,9]. The axion-dilaton and all complex structure moduli are stabilized by fluxes. The remaining 2 Kahler moduli are stabilized by a nonperturbative superpotential, which has been explicitly computed. For this model we identify situations for which a linear combination of the axionic parts of the two Kahler moduli acts as an inflaton. As in our previous scenario, inflation begins at a saddle point of the scalar potential and proceeds as an eternal topological inflation. For a certain range of inflationary parameters, we obtain the COBE-normalized spectrum of metric perturbations and an inflationary scale of M = 3 x 10^{14} GeV. We discuss possible changes of parameters of our model and argue that anthropic considerations favor those parameters that lead to a nearly flat spectrum of inflationary perturbations, which in our case is characterized by the spectral index n_s = 0.95.
TL;DR: In this article, the authors studied the supergravity dual of the a-maximization under AdS5/CFT4 duality, and showed that the trial a-function is the inverse cube of the superpotential of the five-dimensional theory.
TL;DR: In this paper, the supersymmetry conditions for a class of SU(2) structure backgrounds of Type IIB supergravity were analyzed for the AdS/CFT correspondence, which are suitable to describe mass deformations or beta-deformations of four-dimensional superconformal gauge theories.
Abstract: We analyze the supersymmetry conditions for a class of SU(2) structure backgrounds of Type IIB supergravity, corresponding to a specific ansatz for the supersymmetry parameters. These backgrounds are relevant for the AdS/CFT correspondence since they are suitable to describe mass deformations or beta-deformations of four-dimensional superconformal gauge theories. Using Generalized Complex Geometry we show that these geometries are characterized by a closed nowhere-vanishing vector field and a modified fundamental form which is also closed. The vector field encodes the information about the superpotential and the type of deformation - mass or beta respectively. We also show that the Pilch-Warner solution dual to a mass-deformation of = 4 Super Yang-Mills and the Lunin-Maldacena beta-deformation of the same background fall in our class of solutions.
TL;DR: Bouchard et al. as discussed by the authors obtained superpotential tri-linear couplings of the only known globally consistent heterotic minimal supersymmetric standard model, which is based on a slope-stable holomorphic SU (5 ) vector bundle.
TL;DR: In this paper, it was shown that the conformally invariant (3, 4, 1 ) superpotential is generated by the Fayet-Iliopoulos term of the gauge superfield.
TL;DR: In this article, a new class of instanton effects in string compactifications that preserve only = 1 supersymmetry in four dimensions is described, and it is shown that such instantons can also contribute to new multi-fermion and higher-derivative F-terms in the low-energy effective action.
Abstract: We describe a new class of instanton effects in string compactifications that preserve only = 1 supersymmetry in four dimensions. As is well-known, worldsheet or brane instantons in such a background can sometimes contribute to an effective superpotential for the moduli of the compactification. We generalize this phenomenon by showing that such instantons can also contribute to new multi-fermion and higher-derivative F-terms in the low-energy effective action. We consider in most detail the example of heterotic compactification on a Calabi-Yau threefold X with gauge bundle V, in which case we study worldsheet instanton effects that deform the complex structure of the moduli space associated to X and V. We also give new, slightly more economical derivations of some previous results about worldsheet instantons in Type IIA Calabi-Yau compactifications.
TL;DR: In this article, the Schrodinger equation was solved in terms of real orthogonal polynomials and the new solutions were used in the construction of the quantum-mechanical superpotential.
Abstract: The analytic solutions of the one-dimensional Schrodinger equation for the trigonometric Rosen–Morse potential reported in the literature rely upon the Jacobi polynomials with complex indices and complex arguments. We first draw attention to the fact that the complex Jacobi polynomials have non-trivial orthogonality properties which make them uncomfortable for physics applications. Instead we here solve the above equation in terms of real orthogonal polynomials. The new solutions are used in the construction of the quantum-mechanical superpotential.
TL;DR: In this paper, the authors study the 10D equation of motion of dilaton-axion fluctuations in type IIB string compactifications with three-form flux, taking warping into account.
Abstract: We study the 10D equation of motion of dilaton-axion fluctuations in type IIB string compactifications with three-form flux, taking warping into account. Using simplified models with physics comparable to actual compactifications, we argue that the lightest mode localizes in long warped throats and takes a mass of order the warped string scale. Also, the Gukov-Vafa-Witten superpotential is valid for the lightest mass mode; however, the mass is similar to the Kaluza-Klein scale, so the dilaton-axion should be integrated out of the effective theory in this long throat regime (leaving a constant superpotential). On the other hand, there is a large hierarchy between flux-induced and KK mass scales for moderate or weak warping. This hierarchy agrees with arguments given for trivial warping. Along the way, we also estimate the effect of the other 10D supergravity equations of motion on the dilaton-axion fluctuation, since these equations act as constraints. We argue that they give negligible corrections to the simplest approximation.
TL;DR: In this article, the structure of supersymmetric vacua in compactifications of the heterotic string on certain manifolds with SU(3) structure was analyzed and the effective theories associated with compactification on generalized half-flat manifolds were derived.
Abstract: In this paper we analyze the structure of supersymmetric vacua in compactifications of the heterotic string on certain manifolds with SU(3) structure. We first study the effective theories obtained from compactifications on half-flat manifolds and show that solutions which stabilise the moduli at acceptable values are hard to find. We then derive the effective theories associated with compactification on generalized half-flat manifolds. It is shown that these effective theories are consistent with four-dimensional N = 1 supergravity and that the superpotential can be obtained by a Gukov-Vafa-Witten type formula. Within these generalized models, we find consistent supersymmetric (AdS) vacua at weak gauge coupling, provided we allow for general internal gauge bundles. In simple cases we perform a counting of such vacua and find that a fraction of about 1/1000 leads to a gauge coupling consistent with gauge unification.
TL;DR: In this paper, the authors present a formalism for computing the Yukawa couplings in heterotic standard models, which is accomplished by calculating the relevant triple products of cohomology groups, leading to terms proportional to Q *H*u, Q*H*d, L*H *nu and L *Hbar*e in low energy superpotential.
Abstract: In this paper, we present a formalism for computing the Yukawa couplings in heterotic standard models. This is accomplished by calculating the relevant triple products of cohomology groups, leading to terms proportional to Q*H*u, Q*Hbar*d, L*H*nu and L*Hbar*e in the low energy superpotential. These interactions are subject to two very restrictive selection rules arising from the geometry of the Calabi-Yau manifold. We apply our formalism to the "minimal" heterotic standard model whose observable sector matter spectrum is exactly that of the MSSM. The non-vanishing Yukawa interactions are explicitly computed in this context. These interactions exhibit a texture rendering one out of the three quark/lepton families naturally light.
TL;DR: In this article, a coisotropic D8-brane BPS was constructed for the case of a type IIA T6/(2? 2) orientifold, where the magnetic fluxes generated by two D8branes intersect.
Abstract: Up to now chiral type IIA vacua have been mostly based on intersecting D6-branes wrapping special Lagrangian 3-cycles on a CY3 manifold. We argue that there are additional BPS D-branes which have so far been neglected, and which seem to have interesting model-building features. They are coisotropic D8-branes, in the sense of Kapustin and Orlov. The D8-branes wrap 5-dimensional submanifolds of the CY3 which are trivial in homology, but contain a worldvolume flux that induces D6-brane charge on them. This induced D6-brane charge not only renders the D8-brane BPS, but also creates D = 4 chirality when two D8-branes intersect. We discuss in detail the case of a type IIA T6/(2 ? 2) orientifold, where we provide explicit examples of coisotropic D8-branes. We study the chiral spectrum, SUSY conditions, and effective field theory of different systems of D8-branes in this orientifold, and show how the magnetic fluxes generate a superpotential for untwisted K?hler moduli. Finally, using both D6-branes and coisotropic D8-branes we construct new examples of MSSM-like type IIA vacua.
TL;DR: In this paper, the existence of nonsupersymmetric black hole attractor solutions for type II compactification on (the mirror of) CY3(2,128) expressed as a degree-12 hypersurface in WCP4 was studied.
Abstract: We look for possible nonsupersymmetric black hole attractor solutions for type II compactification on (the mirror of) CY3(2,128) expressed as a degree-12 hypersurface in WCP4[1,1,2,2,6]. In the process, (a) for points away from the conifold locus, we show that the existence of a non-supersymmetric attractor along with a consistent choice of fluxes and extremum values of the complex structure moduli, could be connected to the existence of an elliptic curve fibered over C8 which may also be “arithmetic” (in some cases, it is possible to interpret the extremization conditions for the black-hole superpotential as an endomorphism involving complex multiplication of an arithmetic elliptic curve), and (b) for points near the conifold locus, we show that existence of non-supersymmetric black-hole attractors corresponds to a version of A1-singularity in the space Image(Z6R2/Z2 (↪R3)) fibered over the complex structure moduli space. The (derivatives of the) effective black hole potential can be thought of as a real (integer) projection in a suitable coordinate patch of the Veronese map: CP5CP20, fibered over the complex structure moduli space. We also discuss application of Kallosh's attractor equations (which are equivalent to the extremization of the effective black-hole potential) for nonsupersymmetric attractors and show that (a) for points away from the conifold locus, the attractor equations demand that the attractor solutions be independent of one of the two complex structure moduli, and (b) for points near the conifold locus, the attractor equations imply switching off of one of the six components of the fluxes. Both these features are more obvious using the attractor equations than the extremization of the black hole potential.
TL;DR: In this article, the authors present a formalism for computing the Yukawa couplings in heterotic standard models, which is accomplished by calculating the relevant triple products of cohomology groups, leading to terms proportional to Q *H*u, Q*H*d, L*H *nu and L *Hbar*e in low energy superpotential.
Abstract: In this paper, we present a formalism for computing the Yukawa couplings in heterotic standard models. This is accomplished by calculating the relevant triple products of cohomology groups, leading to terms proportional to Q*H*u, Q*Hbar*d, L*H*nu and L*Hbar*e in the low energy superpotential. These interactions are subject to two very restrictive selection rules arising from the geometry of the Calabi-Yau manifold. We apply our formalism to the "minimal" heterotic standard model whose observable sector matter spectrum is exactly that of the MSSM. The non-vanishing Yukawa interactions are explicitly computed in this context. These interactions exhibit a texture rendering one out of the three quark/lepton families naturally light.
TL;DR: In this article, superpotentials for quiver path algebras arising from marginal D-Brane decay on collapsed del Pezzo cycles S in a Calabi-Yau X were derived using the machinery of A{sub {infinity}} products.
Abstract: We compute superpotentials for quiver gauge theories arising from marginal D-Brane decay on collapsed del Pezzo cycles S in a Calabi-Yau X. This is done using the machinery of A{sub {infinity}} products in the derived category of coherent sheaves of X, which in turn is related to the derived category of S and quiver path algebras. We confirm that the superpotential is what one might have guessed from analyzing the moduli space, i.e., it is linear in the fields corresponding to the Exts of the quiver and that each such Ext multiplies a polynomial in Exts equal to precisely the relation represented by the Ext.
TL;DR: In this paper, the authors construct lattice actions for a variety of (2,2) supersymmetric gauge theories in two dimensions with matter fields interacting via a superpotential.
Abstract: We construct lattice actions for a variety of (2,2) supersymmetric gauge theories in two dimensions with matter fields interacting via a superpotential.
TL;DR: In this paper, the configurations of intersecting branes in type IIA string theory corresponding to the meta-stable supersymmetry breaking vacua (hep-th/0608063) in the four-dimensional N=1 supersymmetric Yang-Mills theory coupled massive flavors with adjoint matter where the superpotential has three deformed terms.
Abstract: We present the configurations of intersecting branes in type IIA string theory corresponding to the meta-stable supersymmetry breaking vacua(hep-th/0608063) in the four-dimensional N=1 supersymmetric Yang-Mills theory coupled massive flavors with adjoint matter where the superpotential has three deformed terms.
TL;DR: In this paper, the effect of background fluxes of general Hodge type on the supersymmetry conditions and on the fermionic zero modes on the world-volume of a Euclidean M5/D3-brane in M-theory/type IIB string theory was studied.
Abstract: We study the effect of background fluxes of general Hodge type on the supersymmetry conditions and on the fermionic zero modes on the world-volume of a Euclidean M5/D3-brane in M-theory/type IIB string theory. Using the naive susy variation of the modulino fields to determine the number of zero modes in the presence of a flux of general Hodge type, an inconsistency appears. This inconsistency is resolved by a modification of the supersymmetry variation of the modulinos, which captures the back-reaction of the non-perturbative effects on the background flux and the geometry.
TL;DR: In this paper, it was shown that any shift symmetries introduced to protect the inflaton mass will typically be lifted by threshold corrections to the volume-stabilizing superpotential.
Abstract: Inflationary models whose vacuum energy arises from a D-term are believed not to suffer from the supergravity eta problem of F-term inflation. That is, D-term models have the desirable property that the inflaton mass can naturally remain much smaller than the Hubble scale. We observe that this advantage is lost in models based on string compactifications whose volume is stabilized by a non-perturbative superpotential: the F-term energy associated with volume stabilization causes the eta problem to reappear. Moreover, any shift symmetries introduced to protect the inflaton mass will typically be lifted by threshold corrections to the volume-stabilizing superpotential. Using threshold corrections computed by Berg, Haack, and Kors, we illustrate this point in the example of the D3–D7 inflationary model, and conclude that inflation is possible, but only for fine-tuned values of the stabilized moduli. More generally, we conclude that inflationary models in stable string compactifications, even D-term models with shift symmetries, will require a certain amount of fine-tuning to avoid this new contribution to the eta problem.
TL;DR: In this paper, the authors studied KKLT type models with moduli-mixing superpotential and found that the modulus can be stabilized at a realistic value without tuning 3-form fluxes because of gluino condensation on non-magnetized D-brane.
Abstract: We study KKLT type models with moduli-mixing superpotential. In several string models, gauge kinetic functions are written as linear combinations of two or more moduli fields. Their gluino condensation generates moduli-mixing superpotential. We assume one of moduli fields is frozen already around the string scale. It is found that Kahler modulus can be stabilized at a realistic value without tuning 3-form fluxes because of gluino condensation on (non-)magnetized D-brane. Furthermore, we do not need to highly tune parameters in order to realize a weak gauge coupling and a large hierarchy between the grav- itino mass and the Planck scale, when there exists non-perturbative ef- fects on D3-brane. SUSY breaking patterns in our models have a rich structure. Also, some of our models have cosmologically important implications, e.g., on the overshooting problem and the destabiliza- tion problem due to finite temperature effects as well as the gravitino problem and the moduli problem.
Abstract: A dark energy model with a phantom scalar field, an usual scalar field and the string field theory inspired polynomial potential has been constructed. A two-parameter set of exact solutions to the Friedmann equations has been found. We have constructed such string inspired potential that some exact solutions correspond to the state parameter $w_{DE}>-1$ at large time, whereas other ones correspond to $w_{DE}<-1$ at large time. We demonstrate that the superpotential method is very effective to seek new exact solutions. We also present a two-fields model with a polynomial potential and the state parameter, which crosses the cosmological barrier infinitely often.