Deformations of N=2 superconformal algebra and supersymmetric two-component Camassa-Holm equation

This paper is concerned with a link between central extensions of N = 2 superconformal algebra and a supersymmetric two-component generalization of the Camassa-Holm equation. Deformations of superconformal algebra give rise to two compatible bracket structures. One of the bracket structures is derived from the central extension and admits a momentum operator which agrees with the Sobolev norm of a co-adjoint orbit element. The momentum operator induces, via Lenard relations, a chain of conserved Hamiltonians of the resulting supersymmetric Camassa-Holm hierarchy.

The character of pure spinors

The character of holomorphic functions on the space of pure spinors in 10, 11 and 12 dimensions is calculated. From this character formula, we derive in a manifestly covariant way various central charges which appear in the pure spinor formalism for the superstring. We also derive in a simple way the zero momentum cohomology of the pure spinor BRST operator for the D = 10 and D = 11 superparticle.

Lorentz invariance of the pure spinor BRST cohomology for the superstring

In a previous Letter. The BRST cohomology in the pure spinor formalism of the superstring was shown to coincide with the light-cone Green-Schwarz spectrum by using an SO(8) parameterization of the pure spinor. In this Letter, the SO(9, 1) Lorentz generators are explicitly constructed using this SO(8) parameterization, proving the Lorentz invariance of the pure spinor BRST cohomology. (C) 2001 Published by Elsevier B.V. B.V.

Flat currents in the classical AdS(5) x S-5 pure spinor superstring

It is proven that the classical pure spinor superstring in an AdS(5) X S-5 background has a flat current depending on a continuous parameter. This generalizes the recent result of Bena, et at. for the classical Green-Schwarz superstring.

Pure spinor formalism as an N=2 topological string

Following suggestions of Nekrasov and Siegel, a non-minimal set of fields are added to the pure spinor formalism for the superstring. Twisted (c) over cap = 3 N = 2 generators are then constructed where the pure spinor BRST operator is the fermionic spin-one generator, and the formalism is interpreted as a critical topological string. Three applications of this topological string theory include the super-Poincare covariant computation of multiloop superstring amplitudes without picture-changing operators, the construction of a cubic open superstring field theory without contact-term problems, and a new four-dimensional version of the pure spinor formalism which computes F-terms in the spacetime action.

Pure spinor superspace identities for massless four-point kinematic factors

Using the pure spinor formalism we prove identities which relate the tree-level, one-loop and two-loop kinematic factors for massless four-point amplitudes. From these identities it follows that the complete supersymmetric one- and two-loop amplitudes are immediately known once the tree-level kinematic factor is evaluated. In particular, the two-loop equivalence with the RNS formalism (up to an overall coefficient) is obtained as a corollary.

The higher grading structure of the WKI hierarchy and the two-component short pulse equation

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Effects of time-periodic linear coupling on two-component Bose-Einstein condensates in two dimensions

We examine two-component Gross-Pitaevskii equations with nonlinear and linear couplings, assuming self-attraction in one species and self-repulsion in the other, while the nonlinear inter-species coupling is also repulsive. For initial states with the condensate placed in the self-attractive component, a sufficiently strong linear coupling switches the collapse into decay (in the free space). Setting the linear-coupling coefficient to be time-periodic (alternating between positive and negative values, with zero mean value) can make localized states quasi-stable for the parameter ranges considered herein, but they slowly decay. The 2D states can then be completely stabilized by a weak trapping potential. In the case of the high-frequency modulation of the coupling constant, averaged equations are derived, which demonstrate good agreement with numerical solutions of the full equations. (C) 2007 Elsevier B.V. All rights reserved.

Pure spinors, twistors, and emergent supersymmetry

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

One-loop superstring amplitude from integrals on pure spinors space

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Type I supergravity effective action from pure spinor formalism

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Pure spinor vertex operators in Siegel gauge and loop amplitude regularization

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Notes on the overall coefficient of the two-loop superstring amplitude using pure spinor

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

A new proposal for the picture changing operators in the minimal pure spinor formalism

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)