Five models for lepton mixing

We produce five flavour models for the lepton sector. All five models fit perfectly well - at the 1 sigma level - the existing data on the neutrino mass-squared differences and on the lepton mixing angles. The models are based on the type I seesaw mechanism, on a Z(2) symmetry for each lepton flavour, and either on a (spontaneously broken) symmetry under the interchange of two lepton flavours or on a (spontaneously broken) CP symmetry incorporating that interchange - or on both symmetries simultaneously. Each model makes definite predictions both for the scale of the neutrino masses and for the phase delta in lepton mixing; the fifth model also predicts a correlation between the lepton mixing angles theta(12) and theta(23).

The three-loop SSM beta-functions

We present the supersymmetric standard model three-loop beta-functions for gauge and Yukawa couplings and consider the effect of three-loop corrections on the standard running coupling analyses.

Propriétés géométriques des surfaces associées aux solutions des modèles sigma grassmanniens en deux dimensions

Dans cette thèse, nous analysons les propriétés géométriques des surfaces obtenues des solutions classiques des modèles sigma bosoniques et supersymétriques en deux dimensions ayant pour espace cible des variétés grassmanniennes G(m,n). Plus particulièrement, nous considérons la métrique, les formes fondamentales et la courbure gaussienne induites par ces surfaces naturellement plongées dans l'algèbre de Lie su(n). Le premier chapitre présente des outils préliminaires pour comprendre les éléments des chapitres suivants. Nous y présentons les théories de jauge non-abéliennes et les modèles sigma grassmanniens bosoniques ainsi que supersymétriques. Nous nous intéressons aussi à la construction de surfaces dans l'algèbre de Lie su(n) à partir des solutions des modèles sigma bosoniques. Les trois prochains chapitres, formant cette thèse, présentent les contraintes devant être imposées sur les solutions de ces modèles afin d'obtenir des surfaces à courbure gaussienne constante. Ces contraintes permettent d'obtenir une classification des solutions en fonction des valeurs possibles de la courbure. Les chapitres 2 et 3 de cette thèse présentent une analyse de ces surfaces et de leurs solutions classiques pour les modèles sigma grassmanniens bosoniques. Le quatrième consiste en une analyse analogue pour une extension supersymétrique N=2 des modèles sigma bosoniques G(1,n)=CP^(n-1) incluant quelques résultats sur les modèles grassmanniens. Dans le deuxième chapitre, nous étudions les propriétés géométriques des surfaces associées aux solutions holomorphes des modèles sigma grassmanniens bosoniques. Nous donnons une classification complète de ces solutions à courbure gaussienne constante pour les modèles G(2,n) pour n=3,4,5. De plus, nous établissons deux conjectures sur les valeurs constantes possibles de la courbure gaussienne pour G(m,n). Nous donnons aussi des éléments de preuve de ces conjectures en nous appuyant sur les immersions et les coordonnées de Plücker ainsi que la séquence de Veronese. Ces résultats sont publiés dans la revue Journal of Geometry and Physics. Le troisième chapitre présente une analyse des surfaces à courbure gaussienne constante associées aux solutions non-holomorphes des modèles sigma grassmanniens bosoniques. Ce travail généralise les résultats du premier article et donne un algorithme systématique pour l'obtention de telles surfaces issues des solutions connues des modèles. Ces résultats sont publiés dans la revue Journal of Geometry and Physics. Dans le dernier chapitre, nous considérons une extension supersymétrique N=2 du modèle sigma bosonique ayant pour espace cible G(1,n)=CP^(n-1). Ce chapitre décrit la géométrie des surfaces obtenues des solutions du modèle et démontre, dans le cas holomorphe, qu'elles ont une courbure gaussienne constante si et seulement si la solution holomorphe consiste en une généralisation de la séquence de Veronese. De plus, en utilisant une version invariante de jauge du modèle en termes de projecteurs orthogonaux, nous obtenons des solutions non-holomorphes et étudions la géométrie des surfaces associées à ces nouvelles solutions. Ces résultats sont soumis dans la revue Communications in Mathematical Physics.

Studies in quantum field theory at finite temperature

The thesis deals with certain quantum field systems exhibiting spontaneous symmetry breaking and their response to temperature. These models find application in diverse branches such as particle physics, solid state physics and non~linear optics. The nature of phase transition that these systems may undergo is also investigated. The thesis contains seven chapters. The first chapter is introductory and gives a brief account of the various phenomena associated with spontaneous symmetry breaking. The chapter closes with anote on the effect of temperature on quantum field systems. In chapter 2, the spontaneous symmetry breaking phenomena are reviewed in more detail. Chapter 3, deals with the formulation of ordinary and generalised sine-Gordon field theories on a lattice and the study of the nature of phase transition occurring in these systems. In chapter 4, the effect of temperature on these models is studied, using the effective potential method. Chapter 5 is a continuation of this study for another model, viz, the m6 model. The nature of phase transition is also studied. Chapters 5 and 6 constitute a report of the investigations on the behaviour of coupling constants under thermal excitation D1 $4 theory, scalar electrodynamics, abelian and non-abelian gauge theories

Equivalence between supersymmetric self-dual and Maxwell-Chern-Simons models coupled to a matter spinor superfield

We study the duality of the supersymmetric self-dual and Maxwell-Chern-Simons theories coupled to a fermionic matter superfield, using a master action. This approach evades the difficulties inherent to the quartic couplings that appear when matter is represented by a scalar superfield. The price is that the spinorial matter superfield represents a unusual supersymmetric multiplet, whose main physical properties we also discuss. (C) 2009 Elsevier B.V. All rights reserved.

The Hilbert space of the Chern-Simons theory on a cylinder: a loop quantum gravity approach

As a laboratory for loop quantum gravity, we consider the canonical quantization of the three-dimensional Chern-Simons theory on a noncompact space with the topology of a cylinder. Working within the loop quantization formalism, we define at the quantum level the constraints appearing in the canonical approach and completely solve them, thus constructing a gauge and diffeomorphism invariant physical Hilbert space for the theory. This space turns out to be infinite dimensional, but separable.

Exact renormalization of massless QED(2)

We perform the exact renormalization of two-dimensional massless gauge theories. Using these exact results we discuss the cluster property and confinement in both the anomalous and chiral Schwinger models.

Charges and fluxes in Maxwell theory on compact manifolds with boundary

We investigate the charges and fluxes that can occur in higher-order Abelian gauge theories defined on compact space-time manifolds with boundary. The boundary is necessary to supply a destination to the electric lines of force emanating from brane sources, thus allowing non-zero net electric charges, but it also introduces new types of electric and magnetic flux. The resulting structure of currents, charges, and fluxes is studied and expressed in the language of relative homology and de Rham cohomology and the corresponding abelian groups. These can be organised in terms of a pair of exact sequences related by the Poincare-Lefschetz isomorphism and by a weaker flip symmetry exchanging the ends of the sequences. It is shown how all this structure is brought into play by the imposition of the appropriately generalised Maxwell's equations. The requirement that these equations be integrable restricts the world-volume of a permitted brane (assumed closed) to be homologous to a cycle on the boundary of space-time. All electric charges and magnetic fluxes are quantised and satisfy the Dirac quantisation condition. But through some boundary cycles there may be unquantised electric fluxes associated with quantised magnetic fluxes and so dyonic in nature.

The nonlinear essence of gravitational waves

A critical review of gravitational wave theory is made. It is pointed out that the usual linear approach to the gravitational wave theory is neither conceptually consistent nor mathematically justified. Relying upon that analysis it is argued that-analogously to a Yang-Mills propagating field, which must be nonlinear to carry its gauge charge-a gravitational wave must necessarily be nonlinear to transport its own charge-that is, energy-momentum.

Torsion gravity: A reappraisal

The role played by torsion in gravitation is critically reviewed. After a description of the problems and controversies involving the physics of torsion, a comprehensive presentation of the teleparallel equivalent of general relativity is made. According to this theory, curvature and torsion are alternative ways of describing the gravitational field, and consequently related to the same degrees of freedom of gravity. However, more general gravity theories, like for example Einstein-Cartan and gauge theories for the Poincare and the affine groups, consider curvature and torsion as representing independent degrees of freedom. By using an active version of the strong equivalence principle, a possible solution to this conceptual question is reviewed. This solution ultimately favors the teleparallel point of view, and consequently the completeness of general relativity. A discussion of the consequences for gravitation is presented.

Linear relations between N >= 4 supergravity and subleading-color SYM amplitudes

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Mass and width of a composite Higgs boson

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Dimensional reduction of the ABJM model

We dimensionally reduce the ABJM model, obtaining a two-dimensional theory that can be thought of as a 'master action'. This encodes information about both T- and S-duality, i.e. describes fundamental (F1) and D-strings (D1) in 9 and 10 dimensions. The Higgsed theory at large VEV, (v) over tilde, and large k yields D1-brane actions in 9d and 10d, depending on which auxiliary fields are integrated out. For N = 1 there is a map to a Green-Schwarz string wrapping a nontrivial circle in C(4)/Z(k).

Matsubara-Fradkin thermodynamical quantization of Podolsky electrodynamics

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Generalized soldering of +/- 2 helicity states in D=2+1

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)