Showing papers on "Superpotential published in 1996"

Varieties of vacua in classical supersymmetric gauge theories.

Abstract: We give a simple description of the classical moduli space of vacua for supersymmetric gauge theories with or without a superpotential. The key ingredient in our analysis is the observation that the Lagrangian is invariant under the action of the complexified gauge group ${G}^{c}$. From this point of view the usual $D$-flatness conditions are an artifact of the Wess-Zumino gauge. By using a gauge that preserves ${G}^{c}$ invariance we show that every constant matter field configuration that extremizes the superpotential is ${G}^{c}$ gauge equivalent (in a sense that we make precise) to a unique classical vacuum. This result is used to prove that in the absence of a superpotential the classical moduli space is the algebraic variety described by the set of all holomorphic gauge-invariant polynomials. When a superpotential is present, we show that the classical moduli space is a variety defined by imposing additional relations on the holomorphic polynomials. Many of these points are already contained in the existing literature. The main contribution of the present work is that we give a careful and self-contained treatment of limit points and singularities.

Supersymmetry and Neutrinoless Double Beta Decay

Abstract: Neutrinoless double beta decay (0���) induced by superparticle exchange is investigated. Such a supersymmetric (SUSY) mechanism of 0��� decay arises within SUSY theories with R-parity non-conservation (Rp / ). We consider the minimal supersymmetric standard model (MSSM) with explicit Rp / terms in the superpotential (Rp

A D=4 N=1 Orbifold of Type I Strings

Abstract: We consider the propagation of Type I open superstrings on orbifolds with four non-compact dimensions and $N=1$ supersymmetry. In this paper, we concentrate on a non-trivial Z_2xZ_2 example. We show that consistency conditions, arising from tadpole cancellation and algebraic sources, require the existence of three sets of Dirichlet 5-branes. We discuss fully the enhancements of the spectrum when these 5-branes intersect. An amusing attribute of these models is the importance of the tree-level (in Type I language) superpotential to the consistent relationship between Higgsing and the motions of 5-branes.

Supersymmetric Quantum Cosmology

Abstract: This volume provides a comprehensive and coherent introduction to modern quantum cosmology - the study of the universe as a whole according to the laws of quantum mechanics. In particular, it presents a useful survey of the many profound consequences of supersymmetry (supergravity) in quantum cosmology. After a general introduction to quantum cosmology, the reader is led through Hamiltonian supergravity and canonical quantization and quantum amplitudes through to models of supersymmetric mini superspace and quantum wormholes. The book is rounded off with a look at exciting further developments, including the possible finiteness of supergravity. Ample introductory material is included, ensuring this topical volume is well suited as a graduate text. Researchers in theoretical and mathematical physics, applied maths and cosmology will also find it of immediate interest.

Gravitational Quantum Cohomology

Abstract: We discuss how the theory of quantum cohomology may be generalized to ``gravitational quantum cohomology'' by studying topological sigma models coupled to two-dimensional gravity. We first consider sigma models defined on a general Fano manifold $M$ (manifold with a positive first Chern class) and derive new recursion relations for its two point functions. We then derive bi-Hamiltonian structures of the theories and show that they are completely integrable at least at the level of genus $0$. We next consider the subspace of the phase space where only a marginal perturbation (with a parameter $t$) is turned on and construct Lax operators (superpotentials) $L$ whose residue integrals reproduce correlation functions. In the case of $M=CP^N$ the Lax operator is given by $L= Z_1+Z_2+\cdots +Z_N+e^tZ_1^{-1}Z_2^{-1}\cdots Z_N^{-1}$ and agrees with the potential of the affine Toda theory of the $A_N$ type. We also obtain Lax operators for various Fano manifolds; Grassmannians, rational surfaces etc. In these examples the number of variables of the Lax operators is the same as the dimension of the original manifold. Our result shows that Fano manifolds exhibit a new type of mirror phenomenon where mirror partner is a non-compact Calabi-Yau manifold of the type of an algebraic torus $C^{*N}$ equipped with a specific superpotential.

Supersymmetric Neutrino Masses, R Symmetries, and The Generalized mu Problem

Abstract: In supersymmetric models a tree-level neutrino mass could originate from the (weak-scale) superpotential. We propose and examine a realization of that idea, which arises naturally in the framework of a spontaneously broken U(1) R-symmetry. The solution to the neutrino mass problem could shed light in this framework on the possible resolution of the $\mu$ problem. Furthermore, the suppression of the neutrino mass in comparison to the weak scale arises dynamically and need not be encoded in the superpotential. The latter mechanism operates, for example, in universal models for the soft supersymmetry breaking terms. Phenomenological and cosmological implications of the model are also discussed, some of which are shown to hold more generally. We also note that future signatures could include observable enhancement of dijet and multijet production rates and a correlation between the supersymmetric and neutrino spectra.

A Non-Perturbative Superpotential With $E_8$ Symmetry

Abstract: We compute the non-perturbative superpotential in $F$-theory compactification to four dimensions on a complex three-fold $¶^1\times S$, where $S$ is a rational elliptic surface. In contrast to examples considered previously, the superpotential in this case has interesting modular properties; it is essentially an $E_8$ theta function.

A nonperturbative superpotential with e8-symmetry

Abstract: We compute the nonperturbative superpotential in F-theory compactification to four dimensions on a complex threefold P1×S, where S is a rational elliptic surface. In contrast to examples considered previously, the superpotential in this case has interesting modular properties; it is essentially an E8 theta function.

F-theory, Geometric Engineering and N=1 Dualities

Abstract: We consider geometric engineering of N=1 supersymmetric QFTs with matter in terms of a local model for compactification of F-theory on Calabi-Yau fourfold. By bringing 3-branes near 7-branes we engineer N=1 supersymmetric $SU(N_c)$ gauge theory with $N_f$ flavors in the fundamental. We identify the Higgs branch of this system with the instanton moduli space on the compact four dimensional space of the 7-brane worldvolume. Moreover we show that the Euclidean 3-branes wrapped around the compact part of the 7-brane worldvolume can generate superpotential for $N_f=N_c-1$ as well as lead to quantum corrections to the moduli space for $N_f=N_c$. Finally we argue that Seiberg's duality for N=1 supersymmetric QCD may be mapped to T-duality exchanging 7-branes with 3-branes.

The Minimal Supersymmetric Standard Model

Abstract: The structure of the MSSM is reviewed. We first motivate the particle content of the theory by examining the quantum numbers of the known standard model particles and by the requirement of anomaly cancellation. Once the particle content is fixed we can write down the most general renormalizable superpotential. However such a superpotential will contain terms breaking lepton and baryon number which leads us to the concept of R-parity conservation. The question of supersymmetry breaking is discussed next. We list the possible soft breaking terms. However the Lagrangian involving the most general soft breaking terms is phenomenologically intractable because of the appearance of many new parameters. It also leads to some unacceptable predictions. To reduce the number of parameters we restrict ourselves to the case with universal soft breaking terms at the GUT scale. We motivate the need for universal soft breaking terms by the apparent unification of gauge couplings in the MSSM and by the absence of flavor ch...

Gravity, Particles and Space-Time

Abstract: A gauge-invariant theory of motion of charged test particles, D. Chruscinski and J. Kijowski Heisenberg picture for quantized fields interatcting with nonstationary electromagnetic or gravitational background, A. A. Lobashov and V. M. Mostepanenko general relativity as a gauge theory of orthogonal groups in three dimensions, M. Raiteri et al quantum spacetime , D. Fikelstein et al Jacobi's principle and Hertz' definition of time, H-J Treder et al placing limits on Cartan's torsion from non-Reimannian crystals, L.C. G. de Andrade spinors as differential forms and applications to electromagnetism and quantum mechanics, W. A. Rodrigues and J. Vaz black holes, time arrow and vacuum in quantum electrodynamics, M. E. Gertsenstein one-loop background calculations in the general field theory, P. I. Pronin and K. V. Stepanyantz energy-momentum superpotential in gravitation theory, G. Giachetta and G. Sardanashvily.

Duality in Supersymmetric SU($N_c$) Gauge Theory with Two Adjoint Chiral Superfields

Abstract: We discuss $SU(N_c)$ gauge theory coupled to two adjoint chiral superfields $X$ and $Y$, and a number of fundamental chiral superfields $Q^i$. We add a superpotential that has the form of Arnold's $D$ series $W = \Tr X^{k+1} + \Tr XY^2$. We present a dual description in terms of an $SU(3kN_f - N_c)$ gauge theory, and we show that the duality passes many tests. At the end of the paper, we show how a deformation of this superpotential flows to another duality having a product gauge group $SU(N_c)\times SU(N_c')$, with an adjoint field charged under $SU(N_c)$, an adjoint field charged under $SU(N_c')$, fields in the $(N_c,N_c')$ and $(\overline N_c,\overline N_c')$ representation, and a number of fundamentals. The dual description is an $SU(2kN_f' + kN_f - N_c')\times SU(2kN_f + kN_f' - N_c)$ gauge theory.

Sequence of duals for Sp(2N) supersymmetric gauge theories with adjoint matter.

Abstract: We consider supersymmetric Sp(2{ital N}) gauge theories with {ital F} matter fields in the defining representation, one matter field in the adjoint representation, and no superpotential. We construct a sequence of dual descriptions of this theory using the dualities of Seiberg combined with the {open_quote}{open_quote}deconfinement{close_quote}{close_quote} method introduced by Berkooz. Our duals hint at a new nonperturbative phenomenon that seems to be taking place at asymptotically low energies in these theories: for small {ital F} some of the degrees of freedom form massless, noninteracting bound states while the theory remains in an interacting non-Abelian Coulomb phase. This phenomenon is the result of strong coupling gauge dynamics in the original description, but has a simple classical origin in the dual descriptions. The methods used for constructing these duals can be generalized to any model involving arbitrary two-index tensor representations of Sp(2{ital N}), SO({ital N}), or SU({ital N}) groups. {copyright} {ital 1996 The American Physical Society.}

Minimal Bosonization of supersymmetry

Abstract: The minimal bosonization of supersymmetry in terms of one bosonic degree of freedom is considered. A nontrivial relationship of the construction to the Witten supersymmetric quantum mechanics is illustrated with the help of the simplest N=2 SUSY system realized on the basis of the ordinary (undeformed) bosonic oscillator. It is shown that the generalization of such a construction to the case of Vasiliev deformed bosonic oscillator gives a supersymmetric extension of the two-body Calogero model in the phase of exact or spontaneously broken N=2 SUSY. The construction admits an extension to the case of the OSp(2|2) supersymmetry, and, as a consequence, osp(2|2) superalgebra is revealed as a dynamical symmetry algebra for the bosonized supersymmetric Calogero model. Realizing the Klein operator as a parity operator, we construct the bosonized Witten supersymmetric quantum mechanics. Here the general case of the corresponding bosonized N=2 SUSY is given by an odd function being a superpotential.

Geometric Engineering of N=1 Quantum Field Theories

Abstract: We construct local geometric model in terms of F- and M-theory compactification on Calabi-Yau fourfolds which lead to N=1 Yang-Mills theory in d=4 and its reduction on a circle to d=3. We compute the superpotential in d=3, as a function of radius, which is generated by the Euclidean 5-brane instantons. The superpotential turns out to be the same as the potential for affine Toda theories. In the limit of vanishing radius the affine Toda potential reduces to the Toda potential.