Showing papers on "Superpotential published in 2004"

Fayet-Iliopoulos terms in supergravity and cosmology

Abstract: We clarify the structure of N = 1 supergravity in 1+3 dimensions with constant Fayet?Iliopoulos (FI) terms. The FI terms g? induce non-vanishing R-charges for the fermions and the superpotential. Therefore the D-term inflation model in supergravity with constant FI terms has to be revisited. We present all corrections of order g?/M2P to the classical supergravity action required by local supersymmetry and provide a gauge-anomaly-free version of the model. We also investigate the case of the so-called anomalous U(1) when a chiral superfield is shifted under U(1). In such a case, in the context of string theory, the FI terms originate from the derivative of the K?hler potential and they are inevitably field dependent. This raises an issue of stabilization of the relevant field in applications to cosmology. The recently suggested equivalence between the D-term strings and D-branes of type II theory shows that brane?anti-brane systems produce the FI terms in the effective 4d theory, with the Ramond?Ramond axion shifting under the U(1) symmetry. This connection gives the possibility to interpret many unknown properties of systems in the more familiar language of 4d supergravity D-terms, and vice versa. For instance, the shift of the axion field in both cases restricts the possible forms of the moduli-stabilizing superpotential. We provide some additional consistency checks of the correspondence of D-term strings to D-branes and show that instabilities of the two are closely related. Surviving cosmic D-strings of the type II theory may be potentially observed in the form of D-term strings of 4d supergravity. We study such string solutions of supergravity with constant FI terms with one half supersymmetry unbroken and explain some of the puzzling properties of the zero modes around cosmic strings, such as the difference between the numbers of fermionic and bosonic modes.

Flux Compactifications on Calabi-Yau Threefolds

Abstract: The presence of RR and NS three-form fluxes in type IIB string compactification on a Calabi-Yau orientifold gives rise to a nontrivial superpotential W for the dilaton and complex structure moduli. This superpotential is computable in terms of the period integrals of the Calabi-Yau manifold. In this paper, we present explicit examples of both supersymmetric and nonsupersymmetric solutions to the resulting 4d {Nu} = 1 supersymmetric no-scale supergravity, including some nonsupersymmetric solutions with relatively small values of W. Our examples arise on orientifolds of the hypersurfaces in WP{sub 1,1,1,1,4}{sup 4} and WP{sub 1,1,2,2,6}{sup 4}. They serve as explicit illustrations of several of the ingredients which have played a role in the recent proposals for constructing de Sitter vacua of string theory.

R parity violating minimal supergravity model

Abstract: We present the minimal supersymmetric standard model with general broken R parity, focusing on minimal supergravity (MSUGRA). We discuss the origins of lepton number violation in supersymmetry. We have computed the full set of coupled one-loop renormalization-group equations for the gauge couplings, the superpotential parameters, and for all the soft supersymmetry breaking parameters. We provide analytic formulas for the scalar potential minimization conditions which may be iterated to arbitrary precision. We compute the low-energy spectrum of the superparticles and the neutrinos as a function of the small set of parameters at the unification scale in the general basis. Specializing to MSUGRA, we use the neutrino masses to set new bounds on the R-parity violating couplings. These bounds are up to five orders of magnitude stricter than the previously existing ones. In addition, new bounds on the R-parity violating couplings are also derived demanding a nontachyonic sneutrino spectrum. We investigate the nature of the lightest supersymmetric particle and find extensive regions in parameter space where it is not the neutralino. This leads to a novel set of supersymmetric signatures, which we classify.

Critical Points and Supersymmetric Vacua I

Abstract: Supersymmetric vacua (‘universes’) of string/M theory may be identified with certain critical points of a holomorphic section (the ‘superpotential’) of a Hermitian holomorphic line bundle over a complex manifold. An important physical problem is to determine how many vacua there are and how they are distributed, as the superpotential varies over physically relevant ensembles. In several papers over the last few years, M. R. Douglas and co-workers have studied such vacuum statistics problems for a variety of physical models at the physics level of rigor [Do,AD,DD]. The present paper is the first of a series by the present authors giving a rigorous mathematical foundation for the vacuum statistics problem. It sets down basic results on the statistics of critical points ∇s=0 of random holomorphic sections of Hermitian holomorphic line bundles with respect to a metric connection ∇, when the sections are endowed with a Gaussian measure. The principal results give formulas for the expected density and number of critical points of fixed Morse index of Gaussian random sections relative to ∇. They are particularly concrete for Riemann surfaces. In our subsequent work, the results will be applied to the vacuum statistics problem and to the purely geometric problem of studying metrics which minimize the expected number of critical points.

Heterotic string compactified on half-flat manifolds

Abstract: We study the effective action of the heterotic string compactified on particular half-flat manifolds which arise in the context of mirror symmetry with Neveu-Schwarz\char21{}Neveu-Schwarz flux. We explicitly derive the superpotential and K\"ahler potential at lowest order in ${\ensuremath{\alpha}}^{\ensuremath{'}}$ by a reduction of the bosonic action. The superpotential contains new terms depending on the K\"ahler moduli which originate from the intrinsic geometrical flux of the half-flat manifolds. A generalized Gukov formula, valid for all manifolds with SU(3) structure, is derived from the gravitino mass term. For the half-flat manifolds it leads to a superpotential in agreement with our explicit bosonic calculation. We also discuss the inclusion of gauge fields.

Unitary and complex matrix models as 1-d type 0 strings

Abstract: We propose that the double scaling behavior of the unitary matrix models, and that of the complex matrix models, is related to type 0B and 0A fermionic string theories. The particular backgrounds involved correspond to ĉ < 1 matter coupled to super-Liouville theory. We examine in detail the ĉ = 0 or pure supergravity case, which is related to the double scaling limit around the Gross-Witten transition, and find that reversing the sign of the Liouville superpotential interchanges the 0A and 0B theories. We also find smooth transitions between weakly coupled string backgrounds with D-branes, and backgrounds with Ramond-Ramond fluxes only. Finally, we discuss matrix models with multicritical potentials that are conjectured to correspond to 0A/0B string theories based on (2,4k) super-minimal models.

Conserved charges in Einstein Gauss-Bonnet theory

Abstract: Using Noether's identities, we define a superpotential with respect to a background for the Einstein Gauss–Bonnet theory of gravity. As an example, we show that its associated conserved charge yields the mass-energy of a D-dimensional Gauss–Bonnet black hole in an anti-de Sitter spacetime.

Gaugino Condensation and Nonperturbative Superpotentials in Flux Compactifications

Abstract: There are two known sources of nonperturbative superpotentials for K\"ahler moduli in type IIB orientifolds, or F-theory compactifications on Calabi-Yau fourfolds, with flux: Euclidean brane instantons and low-energy dynamics in D7 brane gauge theories. The first class of effects, Euclidean D3 branes which lift in M-theory to M5 branes wrapping divisors of arithmetic genus 1 in the fourfold, is relatively well understood. The second class has been less explored. In this paper, we consider the explicit example of F-theory on $K3 \times K3$ with flux. The fluxes lift the D7 brane matter fields, and stabilize stacks of D7 branes at loci of enhanced gauge symmetry. The resulting theories exhibit gaugino condensation, and generate a nonperturbative superpotential for K\"ahler moduli. We describe how the relevant geometries in general contain cycles of arithmetic genus $\chi \geq 1$ (and how $\chi > 1$ divisors can contribute to the superpotential, in the presence of flux). This second class of effects is likely to be important in finding even larger classes of models where the KKLT mechanism of moduli stabilization can be realized. We also address various claims about the situation for IIB models with a single K\"ahler modulus.

Localizing gravity on exotic thick 3-branes

Abstract: We consider localization of gravity on thick branes with a nontrivial structure. Double walls that generalize the thick Randall-Sundrum solution, and asymmetric walls that arise from a Z{sub 2} symmetric scalar potential, are considered. We present a new asymmetric solution: a thick brane interpolating between two AdS{sub 5} spacetimes with different cosmological constants, which can be derived from a 'fake supergravity' superpotential, and show that it is possible to confine gravity on such branes.

Superpotentials, A-infinity Relations and WDVV Equations for Open Topological Strings

Abstract: We give a systematic derivation of the consistency conditions which constrain open-closed disk amplitudes of topological strings. They include the A-infinity relations (which generalize associativity of the boundary product of topological field theory), as well as certain homotopy versions of bulk-boundary crossing symmetry and Cardy constraint. We discuss integrability of amplitudes with respect to bulk and boundary deformations, and write down the analogs of WDVV equations for the space-time superpotential. We also study the structure of these equations from a string field theory point of view. As an application, we determine the effective superpotential for certain families of D-branes in B-twisted topological minimal models, as a function of both closed and open string moduli. This provides an exact description of tachyon condensation in such models, which allows one to determine the truncation of the open string spectrum in a simple manner.

Non-critical supergravity (d > 1) and holography

Abstract: In this paper we investigate the supergravity equations of motion associated with non-critical (d > 1) type-II string theories that incorporate RR forms. Using a superpotential formalism we determine several classes of solutions. In particular we find analytic backgrounds with a structure of AdSp + 2 × Sd − p − 2 and numerical solutions that asymptote a linear dilaton with a topology of R1,d − 3 × R × S1. The SUGRA solutions we have found can serve as anti holographic descriptions of gauge theories in a large-N limit which is different than the one of the critical gauge/gravity duality. It is characterized by N → ∞ and gYM2N ~ 1. We have made the first steps in analyzing the corresponding gauge theory properties like Wilson loops and the glue-ball spectra.

D-branes on Calabi{Yau Manifolds and Superpotentials

Abstract: We show how to compute terms in an expansion of the world-volume superpotential for fairly general D-branes on the quintic Calabi-Yau using linear sigma model techniques, and show in examples that this superpotential captures the geometry and obstruction theory of bundles and sheaves on this Calabi-Yau.

Superstrings on AdS_2 and Superconformal Matrix Quantum Mechanics

Abstract: We construct a kappa-symmetric Green-Schwarz action for type IIA string theory on AdS_2. As a candidate holographic dual, we consider superconformal matrix quantum mechanics, given by the Marinari-Parisi model with vanishing or logarithmic superpotential. We derive that the super-eigenvalues form a consistent subsector, and that their dynamics reduces to that of the supersymmetric Calogero-Moser model. The classical string action and the matrix model both have an infinite set of conserved charges, that include an N=2 target space super-Virasoro symmetry. As a microscopic test of the duality, we reproduce the exact form of the Calogero interaction via a string worldsheet calculation.

On the Moduli Dependence of Nonperturbative Superpotentials in Brane Inflation

Abstract: We discuss string corrections to the effective potential in various models of brane inflation. These corrections contribute to the mass of the inflaton candidate and may improve its slow-roll properties. In particular, in orientifold string compactifications with dynamical D3- and D7-branes, the corrections induce inflaton dependence in the part of the superpotential that arises from gaugino condensation or other nonperturbative effects. The additional terms are in part required by supersymmetry. We explicitly discuss D3/D7-inflation, where flat directions of the potential can be lifted, and the KKLMMT model of warped brane inflation, in which the corrections open up the possibility of flattening the potential and canceling unwanted contributions to the inflaton mass.

Analytical solution of the Gross-Neveu model at finite density

Abstract: Recent numerical calculations have shown that the ground state of the Gross-Neveu model at finite density is a crystal. Here, we present the analytical solution of this problem in terms of elliptic functions. The scalar potential is the superpotential of the nonrelativistic Lam\'e Hamiltonian. This model can also serve as an analytically solvable toy model for a relativistic superconductor in the Larkin-Ovchinnikov-Fulde-Ferrell phase.

Are N = 1 and N = 2 supersymmetric quantum mechanics equivalent?

Abstract: After recalling different formulations of the definition of supersymmetric quantum mechanics given in the literature, we discuss the relationships between them in order to provide an answer to the question raised in the title.

Extended Supersymmetries and the Dirac Operator

Abstract: We consider supersymmetric quantum mechanical systems in arbitrary dimensions on curved spaces with nontrivial gauge fields. The square of the Dirac operator serves as Hamiltonian. We derive a relation between the number of supercharges that exist and restrictions on the geometry of the underlying spaces as well as the admissible gauge field configurations. From the superalgebra with two or more real supercharges we infer the existence of integrability conditions and obtain a corresponding superpotential. This potential can be used to deform the supercharges and to determine zero modes of the Dirac operator. The general results are applied to the Kahler spaces CP^n.

Electroweak Symmetry Breaking via UV Insensitive Anomaly Mediation

Abstract: Anomaly mediation solves the supersymmetric flavor and CP problems. This is because the superconformal anomaly dictates that supersymmetry breaking is transmitted through nearly flavor-blind infrared physics that is highly predictive and UV insensitive. Slepton mass squareds, however, are predicted to be negative. This can be solved by adding D-terms for $\mathrm{U}{(1)}_{Y}$ and $\mathrm{U}{(1)}_{B\ensuremath{-}L}$ while retaining the UV insensitivity. In this paper we consider electroweak symmetry breaking via UV insensitive anomaly mediation in several models. For the minimal supersymmetric standard model we find a stable vacuum when $\mathrm{tan}\ensuremath{\beta}l1,$ but in this region the top Yukawa coupling blows up only slightly above the supersymmetry breaking scale. For the next-to-minimal supersymmetric standard model (NMSSM), we find a stable electroweak breaking vacuum but with a chargino that is too light. Replacing the cubic singlet term in the NMSSM superpotential with a term linear in the singlet we find a stable vacuum and viable spectrum. Most of the parameter region with correct vacua requires a large superpotential coupling, precisely what is expected in the ``Fat Higgs'' model in which the superpotential is generated dynamically. We have therefore found the first viable UV complete, UV insensitive supersymmetry breaking model that solves the flavor and CP problems automatically: the Fat Higgs model with UV insensitive anomaly mediation. Moreover, the cosmological gravitino problem is naturally solved, opening up the possibility of realistic thermal leptogenesis.