Lie symmetry analysis and reductions of a two-dimensional integrable generalization of the Camassa-Holm equation

In this Letter we investigate Lie symmetries of a (2 + 1)-dimensional integrable generalization of the Camassa-Holm (CH) equation. Through the similarity reductions we obtain four different (1 + 1)-dimensional systems of partial differential equations in which one of them turns out to be a (1 + 1)-dimensional CH equation. We establish their integrability by providing the Lax pair for all of them. Further, we present a brief analysis for some types of particular solutions which include the cuspon, peakon and soliton solutions for the two-dimensional generalization of the CH equation. (C) 2000 Published by Elsevier B.V. B.V.

Closing the SU(3)(L)circle times U(1)(X) symmetry at the electroweak scale

We show that some models with SU(3)(C)circle times SU(3)(L)circle times U(1)(X) gauge symmetry can be realized at the electroweak scale and that this is a consequence of an approximate global SU(2)(L+R) symmetry. This symmetry implies a condition among the vacuum expectation value of one of the neutral Higgs scalars, the U(1)(X)'s coupling constant, g(X), the sine of the weak mixing angle sin theta(W), and the mass of the W boson, M-W. In the limit in which this symmetry is valid it avoids the tree level mixing of the Z boson of the standard model with the extra Z(') boson. We have verified that the oblique T parameter is within the allowed range indicating that the radiative corrections that induce such a mixing at the 1-loop level are small. We also show that a SU(3)(L+R) custodial symmetry implies that in some of the models we have to include sterile (singlets of the 3-3-1 symmetry) right-handed neutrinos with Majorana masses, since the seesaw mechanism is mandatory to obtain light active neutrinos. Moreover, the approximate SU(2)(L+R)subset of SU(3)(L+R) symmetry implies that the extra nonstandard particles of these 3-3-1 models can be considerably lighter than it had been thought before so that new physics can be really just around the corner.

Symmetry analysis of an integrable reaction-diffusion equation

In this paper, we investigate the invariance and integrability properties of an integrable two-component reaction-diffusion equation. We perform Painleve analysis for both the reaction-diffusion equation modelled by a coupled nonlinear partial differential equations and its general similarity reduced ordinary differential equation and confirm its integrability. Further, we perform Lie symmetry analysis for this model. Interestingly our investigations reveals a rich variety of particular solutions, which have not been reported in the literature, for this model. (C) 2000 Elsevier B.V. Ltd. All rights reserved.

Gravitation and duality symmetry

By generalizing the Hodge dual operator to the case of soldered bundles, and working in the context of the teleparallel equivalent of general relativity, an analysis of the duality symmetry in gravitation is performed. Although the basic conclusion is that, at least in the general-case, gravitation is not dual symmetric, there is a particular theory in which this symmetry shows up. It is a self dual (or anti-self dual) teleparallel gravity in which, due to the fact that it does not contribute to the interaction of fermions with gravitation, the purely tensor part of torsion is assumed to vanish. The ensuing fermionic gravitational interaction is found to be chiral. Since duality is intimately related to renormalizability, this theory may eventually be more amenable to renormalization than telepaxallel gravity or general relativity.

Quark clustering and chiral symmetry breaking in nuclear matter

Chiral symmetry breaking at finite baryon density is usually discussed in the context of quark matter, i.e. a system of deconfined quarks. Many systems like stable nuclei and neutron stars however have quarks confined within nucleons. In this paper we construct a Fermi sea of three-quark nucleon clusters and investigate the change of the quark condensate as a function of baryon density. We study the effect of quark clustering on the in-medium quark condensate and compare results with the traditional approach of modeling hadronic matter in terms of a Fermi sea of deconfined quarks.

Vertex operators and soliton solutions of affine Toda model with U(2) symmetry

The symmetry structure of the non-Abelian affine Toda model based on the coset SL(3)/SL(2) circle times U(1) is studied. It is shown that the model possess non-Abelian Noether symmetry closing into a q-deformed SL(2) circle times U(1) algebra. Specific two-vertex soliton solutions are constructed.

Local duality and charge symmetry violation in quark distributions

We use local quark-hadron duality to calculate the nucleon structure function as seen by neutrino and muon beams. Our result indicates a possible signal of charge symmetry violation at the parton level in the very large x region.

Chiral-symmetry restoration in clustered hadronic matter

Chiral-symmetry restoration is usually discussed in the context of quark matter, a system of deconfined quarks. However, many systems like stable nuclei and neutron stars have quarks confined within nucleons. In the present paper we use a Fermi sea of three-quark clusters instead of a Fermi sea of deconfined quarks to investigate the in-medium quark condensate. We find that an enhancement of the chiral breaking in clustered matter as claimed in the literature is not a consequence of the clustering but rather dependent on the microscopic model dynamics.

Custodial symmetry and extensions of the standard model

We show that the extension of the approximate custodial SU(2)(L+R) global symmetry to all the Yukawa interactions of the standard model Lagrangian implies the introduction of sterile right-handed neutrinos and the seesaw mechanism in this sector. In this framework, the observed quark and lepton masses may be interpreted as an effect of physics beyond the standard model. The mechanism used for breaking this symmetry in the Yukawa sector could be different from the one at work in the vector boson sector. We give three model independent examples of these mechanisms.

Gravitation and the local symmetry group of space-time

According to general relativity, the interaction of a matter field with gravitation requires the simultaneous introduction of a tetrad field, which is a field related to translations, and a spin connection, which is a field assuming values in the Lie algebra of the Lorentz group. These two fields, however, are not independent. By analyzing the constraint between them, it is concluded that the relevant local symmetry group behind general relativity is provided by the Lorentz group. Furthermore, it is shown that the minimal coupling prescription obtained from the Lorentz covariant derivative coincides exactly with the usual coupling prescription of general relativity. Instead of the tetrad, therefore, the spin connection is to be considered as the fundamental field representing gravitation.

Chiral symmetry and pion-nucleon scattering

In this work, we study the influence of the way pious couple to nucleons in perturbative calculation of an observable in the pion-nucleon scattering.

Dual superconformal symmetry, and the amplitude/Wilson loop connection

We show that tree level superstring theories on certain supersymmetric backgrounds admit a symmetry which we call "fermionic T-duality". This is a non-local redefinition of the fermionic worldsheet fields similar to the redefinition we perform on bosonic variables when we do an ordinary T-duality. This duality maps a supersymmetric background to another supersymmetric background with different RR fields and a different dilaton. We show that a certain combination of bosonic and fermionic T-dualities maps the full superstring theory on AdS(5) x S-5 back to itself in such a way that gluon scattering amplitudes in the original theory map to something very close to Wilson loops in the dual theory. This duality maps the "dual superconformal symmetry" of the original theory to the ordinary superconformal symmetry of the dual model. This explains the dual superconformal invariance of planar scattering amplitudes of N = 4 super Yang Mills and also sheds some light on the connection between amplitudes and Wilson loops. In the appendix, we propose a simple prescription for open superstring MHV tree amplitudes in a flat background.

ON FERMION MASSES and MIXING IN A MODEL WITH A(4) SYMMETRY

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

A symmetry reduction technique for higher order Painleve systems

The symmetry reduction of higher order Painleve systems is formulated in terms of Dirac procedure. A set of canonical variables that admit Dirac reduction procedure is proposed for Hamiltonian structures governing the A(2M)((1)) and A(2M-1)((1)) Painleve systems for M = 2,3,.... (C) 2012 Elsevier B.V. All rights reserved.

Three-Higgs-doublet model with A(4) symmetry

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)