Free field realizations of the elliptic affine Lie algebra sl(2, R) circle plus (Omega(R)/dR)

In this paper we construct two free field realizations of the elliptic affine Lie algebra sl(2, R) circle plus Omega(R)/dR where R = C[t. t(-1), u vertical bar u(2) = t(3) - 2bt(2) + t]. The first realization provides an analogue of Wakimoto`s construction for Affine Kac-Moody algebras, but in the setting of the elliptic affine Lie algebra. The second realization gives new types of representations analogous to Imaginary Verma modules in the Affine setting. (c) 2009 Elsevier B.V. All rights reserved.

Signatures of doubly charged Higgs in the SU(3)(L) circle times U(1)(N) model at the CERN LHC

The scalar sector of the simplest version of the 3-3-1 electroweak model is constructed with three Higgs triplets only. We show that a relation involving two of the constants of the model, two vacuum expectation values of the neutral scalars, and the mass of the doubly charged Higgs boson leads to important information concerning the signals of this scalar particle.

Neutral Higgs bosons in the SU(3)(L)circle times U(1)(N) model

The SU(3)(L)circle times U(1)(N) electroweak model predicts new Higgs bosons beyond the one of the standard model. In this work we investigate the signature and production of neutral SU(3)(L)circle times U(1)(N) Higgs bosons in the e(-)e(+) Next Linear Collider and in the CERN Linear Collider . We compute the branching ratios of two of the SU(3)(L)circle times U(1)(N) neutral Higgs bosons and study the possibility to detect them and the Z' extra neutral boson of the model.

Naturally light invisible axion and local Z(13)circle times Z(3) symmetries

We show that by imposing local Z(13)circle timesZ(3) symmetries in an SU(2)circle timesU(1) electroweak model we can implement an invisible axion in such a way that (i) the Peccei-Quinn symmetry is an automatic symmetry of the classical Lagrangian, and (ii) the axion is protected from semiclassical gravitational effects. In order to be able to implement such a large discrete symmetry, and at the same time allow a general mixing in each charge sector, we introduce right-handed neutrinos and enlarge the scalar sector of the model. The domain wall problem is briefly considered.

SU(5)circle times Z(13) grand unification model

We propose an SU(5) grand unified model with an invisible axion and the unification of the three coupling constants which is in agreement with the values, at M(Z), of alpha, alpha(s), and sin(2)theta(W). A discrete, anomalous, Z(13) symmetry implies that the Peccei-Quinn symmetry is an automatic symmetry of the classical Lagrangian protecting, at the same time, the invisible axion against possible semiclassical gravity effects. Although the unification scale is of the order of the Peccei-Quinn scale the proton is stabilized by the fact that in this model the standard model fields form the SU(5) multiplets completed by new exotic fields and, also, because it is protected by the Z(13) symmetry.

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.

A statistical law for multiplicities of SU(3) irreps (lambda, mu) in the plethysm {eta} circle times(3) {m} -> (lambda, mu)

A statistical law for the multiplicities of the SU(3) irreps (lambda, mu) in the reduction of totally symmetric irreducible representations {m} of U(N), N = (eta + 1) (eta + 2)/2 with eta being the three-dimensional oscillator major shell quantum number, is derived in terms of the quadratic and cubic invariants of SU(3), by determining the first three terms of an asymptotic expansion for the multiplicities. To this end, the bivariate Edgeworth expansion known in statistics is used. Simple formulae, in terms of m and eta, for all the parameters in the expansion are derived. Numerical tests with large m and eta = 4, 5 and 6 show good agreement with the statistical formula for the SU(3) multiplicities.

Fixed points on torus fiber bundles over the circle

The main purpose of this work is to study fixed points of fiber-preserving maps over the circle S-1 for spaces which axe fibrations over S-1 and the fiber is the torus T. For the case where the fiber is a surface with nonpositive Euler characteristic, we establish general algebraic conditions, in terms of the fundamental group and the induced homomorphism, for the existence of a deformation of a map over S-1 to a fixed point, free map. For the case where the fiber is a torus, we classify all maps over S-1 which can be deformed fiberwise to a fixed point free map.

Fixed points on Klein bottle fiber bundles over the circle

The main purpose of this work is to study fixed points of fiber-preserving maps over the circle S(1) for spaces which are fiber bundles over S(1) and the fiber is the Klein bottle K. We classify all such maps which can be deformed fiberwise to a fixed point free map. The similar problem for torus fiber bundles over S(1) has been solved recently.

FLAVOR-CHANGING NEUTRAL CURRENTS IN SU(3)L-CIRCLE-TIMES-U(1)Y MODELS

We consider flavor changing neutral current effects coming from the Z' exchange in 3-3-1 models. We show that the mass of this extra neutral vector boson may be less than 2 TeV and discuss the problem of quark family discrimination.

Path formulation for Z(2) circle plus Z(2)-equivariant bifurcation problems

M. Manoel and I. Stewart 0101) classify Z(2) circle plus Z(2)-equivariant bifurcation problems up to codimension 3 and 1 modal parameter, using the classical techniques of singularity theory of Golubistky and Schaeffer [8]. In this paper we classify these same problems using an alternative form: the path formulation (Theorem 6.1). One of the advantages of this method is that the calculates to obtain the normal forms are easier. Furthermore, in our classification we observe the presence of only one modal parameter in the generic core. It differs from the classical classification where the core has 2 modal parameters. We finish this work comparing our classification to the one obtained in [10].