Synchronization and Non-Smooth Dynamical Systems

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Regularization and singular perturbation techniques for non-smooth systems

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Unconstrained variables of non-commutative open strings

The boundary conditions of the bosonic string theory in non-zero B-field background are equivalent to the second class constraints of a discretized version of the theory. By projecting the original canonical coordinates onto the constraint surface we derive a set of coordinates of string that are unconstrained. These coordinates represent a natural framework for the quantization of the theory.

One loop conformal invariance of the superstring in an AdS(5) x S-5 background

It is proven that the pure spinor superstring in an AdS(5) x S-5 background remains conformally invariant at one loop level in the sigma model perturbation theory.

Spinning Hopf solitons on S-3 x R

We consider a field theory with target space being the two dimensional sphere S-2 and defined on the space-time S-3 x R. The Lagrangean is the square of the pull-back of the area form on S-2. It is invariant under the conformal group SO(4, 2) and the infinite dimensional group of area preserving diffeomorphisms of S-2. We construct an infinite number of exact soliton solutions with non-trivial Hopf topological charges. The solutions spin with a frequency which is bounded above by a quantity proportional to the inverse of the radius of S-3. The construction of the solutions is made possible by an ansatz which explores the conformal symmetry and a U(1) subgroup of the area preserving diffeomorphism group.

Metric-scalar gravity with torsion and the measurability of the non-minimal coupling

The measurability of the non-minimal coupling is discussed by considering the correction to the Newtonian static potential in the semiclassical approach. The coefficient of the gravitational Darwin term (GDT) gets redefined by the non-minimal torsion scalar couplings. Based on a similar analysis of the GDT in the effective field theory approach to non-minimal scalar, we conclude that for reasonable values of the couplings the correction is very small.

General unitary SU(1,1) TFD formulation

In this Letter we discuss a generalization for the thermal Bogoliubov transformation in the context of a Hermitian general SU(1,1) transformation generator. The TFD tilde conjugation rules are redefined using an appropriated Tomita-Takesaki modular operator. (C) 2003 Elsevier B.V. All rights reserved.

Taming the b antighost with Ramond-Ramond flux

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

Non-local effects at the onset of the chiral transition

Inspired by analytic results obtained for a systematic expansion of the memory kernel in dissipative quantum mechanics, we propose a phenomenological procedure to incorporate non-markovian corrections to the Langevin dynamics of an order parameter in field theory systematically. In this note, we restrict our analysis to the onset of the evolution. As an example, we consider the process of phase conversion in the chiral transition.

Confinement, solitons and the equivalence between the sine-Gordon and massive Thirring models

We consider a two-dimensional integrable and conformally invariant field theory possessing two Dirac spinors and three scalar fields. The interaction couples bilinear terms in the spinors to exponentials of the scalars. Its integrability properties are based on the sl(2) affine Kac-Moody algebra, and it is a simple example of the so-called conformal affine Toda theories coupled to matter fields. We show, using bosonization techniques, that the classical equivalence between a U(1) Noether current and the topological current holds true at the quantum level, and then leads to a bag model like mechanism for the confinement of the spinor fields inside the solitons. By bosonizing the spinors we show that the theory decouples into a sine-Gordon model and free scalars. We construct the two-soliton solutions and show that their interactions lead to the same time delays as those for the sine-Gordon solitons. The model provides a good laboratory to test duality ideas in the context of the equivalence between the sine-Gordon and Thirring theories. © 2000 Elsevier Science B.V. All rights reserved.

One loop conformal invariance of the superstring in an AdS5 × S5 background

It is proven that the pure spinor superstring in an AdS5 × S5 background remains conformally invariant at one loop level in the sigma model perturbation theory. © SISSA/ISAS 2003.

Conformal invariance of the pure spinor superstring in a curved background

It is shown that the pure spinor formulation of the heterotic superstring in a generic gravitational and super Yang-Mills background has vanishing one-loop beta functions. © SISSA/ISAS 2004.

Spinning Hopf solitons on S3 × ℝ

We consider a field theory with target space being the two dimensional sphere S2 and defined on the space-time S3 × . The Lagrangean is the square of the pull-back of the area form on S2. It is invariant under the conformal group SO(4,2) and the infinite dimensional group of area preserving diffeomorphisms of S2. We construct an infinite number of exact soliton solutions with non-trivial Hopf topological charges. The solutions spin with a frequency which is bounded above by a quantity proportional to the inverse of the radius of S3. The construction of the solutions is made possible by an ansatz which explores the conformal symmetry and a U(1) subgroup of the area preserving diffeomorphism group. © SISSA 2006.

One-loop conformal invariance of the type II pure spinor superstring in a curved background

We compute the one-loop beta functions for the Type II superstring using the pure spinor formalism in a generic supergravity background. It is known that the classical pure spinor BRST symmetry puts the background fields on-shell. In this paper we show that the one-loop beta functions vanish as a consequence of the classical BRST symmetry of the action. © SISSA 2007.

A construction of integrated vertex operator in the pure spinor sigma-model in AdS(5) x S-5

Vertex operators in string theory me in two varieties: integrated and unintegrated. Understanding both types is important for the calculation of the string theory amplitudes. The relation between them is a descent procedure typically involving the b-ghost. In the pure spinor formalism vertex operators can be identified as cohomology classes of an infinite-dimensional Lie superalgebra formed by covariant derivatives. We show that in this language the construction of the integrated vertex from an unintegrated vertex is very straightforward, and amounts to the evaluation of the cocycle on the generalized Lax currents.