Inter-relations between additive shape invariant superpotentials

All known additive shape invariant superpotentials in nonrelativistic quantum mechanics belong to one of two categories: superpotentials that do not explicitly depend on ħ, and their ħ-dependent extensions. The former group themselves into two disjoint classes, depending on whether the corresponding Schrödinger equation can be reduced to a hypergeometric equation (type-I) or a confluent hypergeometric equation (type-II). All the superpotentials within each class are connected via point canonical transformations. Previous work [19] showed that type-I superpotentials produce type-II via limiting procedures. In this paper we develop a method to generate a type I superpotential from type II, thus providing a pathway to interconnect all known additive shape invariant superpotentials.     

Effective Superpotentials for Compact D5-Brane Calabi-Yau Geometries

For compact Calabi-Yau geometries with D5-branes we study N = 1 effective superpotentials depending on both open- and closed-string fields. We develop methods to derive the open/closed Picard-Fuchs differential equations, which control D5-brane deformations as well as complex structure deformations of the compact Calabi-Yau space. Their solutions encode the flat open/closed coordinates and the effective superpotential. For two explicit examples of compact D5-brane Calabi-Yau hypersurface geometries we apply our techniques and express the calculated superpotentials in terms of flat open/closed coordinates. By evaluating these superpotentials at their critical points we reproduce the domain wall tensions that have recently appeared in the literature. Finally we extract orbifold disk invariants from the superpotentials, which, up to overall numerical normalizations, correspond to orbifold disk Gromov-Witten invariants in the mirror geometry.     

Covariantized Nœther identities and conservation laws for perturbations in metric theories of gravity

A construction of conservation laws and conserved quantities for perturbations in arbitrary metric theories of gravity is developed. In an arbitrary field theory, with the use of incorporating an auxiliary metric into the initial Lagrangian covariantized N?ther identities are carried out. Identically conserved currents with corresponding superpotentials are united into a family. Such a generalized formalism of the covariantized identities gives a natural basis for constructing conserved quantities for perturbations. A new family of conserved currents and correspondent superpotentials for perturbations on arbitrary curved backgrounds in metric theories is suggested. The conserved quantities are both of pure canonical N?ther and of Belinfante corrected types. To test the results each of the superpotentials of the family is applied to calculate the mass of the Schwarzschild-anti-de Sitter black hole in the Einstein–Gauss–Bonnet gravity. Using all the superpotentials of the family gives the standard accepted mass.     

Supersymmetry, PT-symmetry and spectral bifurcation

We demonstrate that large class of PT-symmetric complex potentials, which can have isospectral real partner potentials, possess two different superpotentials. In the parameter domain, where the superpotential is unique, the spectrum is real and shape-invariant, leading to translational shift in a suitable parameter by real units. The case of two different superpotentials, leading to same potential, yields broken PT-symmetry, the energy spectra in the two phases being separated by a bifurcation. Interestingly, these two superpotentials generate the two disjoint sectors of the Hilbert space. In the broken case, shape invariance produces complex parametric shifts.     

Generation of a complete set of additive shape-invariant potentials from an Euler equation

In supersymmetric quantum mechanics, shape invariance is a sufficient condition for solvability. We show that all conventional additive shape-invariant superpotentials that are independent of ? can be generated from two partial differential equations. One of these is equivalent to the one-dimensional Euler equation expressing momentum conservation for inviscid fluid flow, and it is closed by the other. We solve these equations, generate the set of all conventional shape-invariant superpotentials, and show that there are no others in this category. We then develop an algorithm for generating all additive shape-invariant superpotentials including those that depend on ? explicitly.     

Dynamics of N = 2 supersymmetric gauge theories in three dimensions

We study the structure of the moduli spaces of vacua and superpotentials of N = 2 supersymmetric gauge theories in three dimensions. By analyzing the instanton corrections, we compute the exact superpotentials and determine the quantum Coulomb and Higgs branches of the theories in the weak coupling regions. We find candidates for non-trivial N = 2 superconformal field theories at the singularities of the moduli spaces. The analysis is carried out explicitly for gauge groups U(N_c) and SU(N_c) with N _f flavors. We show that the field theory results are in complete agreement with the intersecting branes picture. We also compute the exact superpotentials for arbitrary gauge groups and arbitrary matter content.     

Relative periods and open-string integer invariants for a compact Calabi–Yau hypersurface

In this work we compute relative periods for B-branes, realized in terms of divisors in a compact Calabi–Yau hypersurface, by means of direct integration. Although we exemplify the method of direct integration with a particular Calabi–Yau geometry, the recipe automatically generalizes for divisors in other Calabi–Yau geometries as well. From the calculated relative periods we extract double-logarithmic periods. These periods qualify to describe disk instanton generated N=1 superpotentials of the corresponding compact mirror Calabi–Yau geometry in the large volume regime. Finally we extract the integer invariants encoded in these brane superpotentials.     

Gauge mediation simplified

Gauge mediation of supersymmetry breaking is drastically simplified using generic superpotentials without U(1)R symmetry by allowing metastable vacua.     

Comment on ‘Supersymmetry, PT-symmetry and spectral bifurcation’

We demonstrate that the recent paper by Abhinav and Panigrahi entitled ‘Supersymmetry, PT-symmetry and spectral bifurcation’ [K. Abhinav, P.K. Panigrahi, Ann. Phys. 325 (2010) 1198], which considers two different types of superpotentials for the PT-symmetric complexified Scarf II potential, fails to take into account the invariance under the exchange of its coupling parameters. As a result, they miss the important point that for unbroken PT-symmetry this potential indeed has two series of real energy eigenvalues, to which one can associate two different superpotentials. This fact was first pointed out by the present authors during the study of complex potentials having a complex sl(2) potential algebra.     

Second invariant for two-dimensional classical super systems

Construction of superpotentials for two-dimensional classical super systems (forN > 2) is carried out. Some interesting potentials have been studied in their super form and also their integrability.     

Gauge natural formulation of conformal gravity

We consider conformal gravity as a gauge natural theory. We study its conservation laws and superpotentials. We also consider the Mannheim and Kazanas spherically symmetric vacuum solution and discuss conserved quantities associated to conformal and diffeomorphism symmetries.     

Superpotentials of $\mathcal{N}=1$ SUSY gauge theories

The European Physical Journal C - An introduction to recent advances in computing effective superpotentials of four dimensional $\mathcal{N}=1$ SUSY gauge theories coupled to matter is presented....     

Dirac Equation and Ground State of Solvable Potentials: Supersymmetry Method

The supersymmetry in non-relativistic quantum mechanics is applied as an algebraic method to obtain the solutions of the Dirac equation with spherical symmetry electromagnetic potentials. We show that some of the superpotentials related to ground state of the solvable potentials in non-relativistic quantum mechanics can be used for studying of the Dirac equation.     

Preface

In this article, a family of periodic quantum Hamiltonians, that is subject to a closure condition is considered. In the context of the factorization method, we address the question of non-uniqueness of the governing superpotentials and study an alternative factorization to generate new hierarchies of potentials.     

On partner potentials in parasupersymmetric quantum mechanics

The constraint on the two superpotentials characterizing a parasuperhamiltonian is shown to be a Riccati equation which helps us for studying partner potentials. We point out that only three different types of parasuperspectra can appear. The simplest type admitting a unique non degenerate zero energy value can be associated with different models already discussed in other contexts.     

Intersoliton forces in the Wess–Zumino model

The spectrum of supersymmetric domain wall solitons of the Wess–Zumino model is known to be discontinuous across a curve (of marginal stability) in the moduli space of quartic superpotentials. Here we show how this phenomenon can be understood from the behaviour of the long-range inter-soliton force, which we compute by a method due to Manton.     

General Covariant Conservation Law of Angular Momentum in General Relativity

The conservative Noether current corresponding to the invariance of the action of a gravitymatter system under the local Lorentz transformation can be interpreted as the angular momentum tensor of the system. The existence of superpotentials which are expressed in terms of the vierbein only makes the totd current iden ticdy conserved and the total angular momentum gauge-covariant. Two examples are given. It is shown that this conservation law of angular momentum in general relativity is reasonable.     

Pauli fermions as components of D=2 supersymmetrical quantum mechanics

We consider the Pauli hamiltonian for charged fermions in electromagnetic and scalar potentials as being a component of the D=2 supersymmetrical hamiltonian. The admissible class of electromagnetic potentials is described. For a subclass of such potentials the fermion spectrum consists of pairs of equally splitted levels. The double degeneracy of levels (the sign of hidden supersymmetry) arises for holomorphic superpotentials.     

Mirror symmetry,D-brane superpotentials and Ooguri-Vafa invariants of Calabi-Yau manifolds

The D-brane superpotential is very important in the low energy effective theory.As the generating function of all disk instantons from the worldsheet point of view,it plays a crucial role in deriving some important properties of the compact Calabi-Yau manifolds.By using the generalized GKZ hypergeometric system,we will calculate the D-brane superpotentials of two non-Fermat type compact Calabi-Yau hypersurfaces in toric varieties,respectively.Then according to the mirror symmetry,we obtain the A-model superpotentials and the Ooguri-Vafa invariants for the mirror Calabi-Yau manifolds.     

One-loop effective potential in N=12 generic chiral superfield model

We obtain the one-loop quantum corrections to the Kählerian and superpotentials in the generic chiral superfield model on the nonanticommutative superspace. Unlike all previous works, we use a method which does not require to rewrite a star-product of superfields in terms of ordinary products. In the Kählerian potential sector the one-loop contributions are analogous to ones in the undeformed theory while in the chiral potential sector the quantum corrections contain a deformation parameter.