Étude des transitions de phases dans le modèle de Higgs abélien en (2+1) dimensions et l'effet du terme de Chern-Simons

Nous avons investigué, via les simulations de Monte Carlo, les propriétés non-perturbatives du modèle de Higgs abélien en 2+1 dimensions sans et avec le terme de Chern-Simons dans la phase de symétrie brisée, en termes de ses excitations topologiques: vortex et anti-vortex. Le but du présent travail est de rechercher les phases possibles du système dans ce secteur et d'étudier l'effet du terme de Chern-Simons sur le potentiel de confinement induit par les charges externes trouvé par Samuel. Nous avons formulé une description sur réseau du modèle effectif en utilisant une tesselation tétraédrique de l'espace tridimensionnel Euclidien pour générer des boucles de vortex fermées. En présence du terme de Chern-Simons, dans une configuration donnée, nous avons formulé et calculé le nombre d'enlacement entre les différentes boucles de vortex fermées. Nous avons analysé les propriétés du vide et calculé les valeurs moyennes de la boucle de Wilson, de la boucle de Polyakov à différentes températures et de la boucle de 't Hooft en présence du terme de Chern-Simons. En absence du terme de Chern-Simons, en variant la masse des boucles de vortex, nous avons trouvé deux phases distinctes dans le secteur de la symétrie brisée, la phase de Higgs habituelle et une autre phase caractérisée par l'apparition de boucles infinies. D'autre part, nous avons trouvé que la force entre les charges externes est écrantée correpondant à la loi périmètre pour la boucle de Wilson impliquant qu'il n'y a pas de confinement. Cependant, après la transition, nous avons trouvé qu'il existe toujours une portion de charges externes écrantée, mais qu'après une charge critique, l'énergie libre diverge. En présence du terme de Chern-Simons, et dans la limite de constante de couplage faible de Chern-Simons nous avons trouvé que les comportements de la boucle de Wilson et de la boucle de 't Hooft ne changent pas correspondants à une loi périmètre, impliquant qu'il n'y a pas de confinement. De plus, le terme de Chern-Simons ne contribue pas à la boucle de Wilson.

Énergie des vortex dans un modèle abélien de Higgs en 2+1 dimensions avec un potentiel d’ordre six

Dans ce travail, j’étudierai principalement un modèle abélien de Higgs en 2+1 dimensions, dans lequel un champ scalaire interagit avec un champ de jauge. Des défauts topologiques, nommés vortex, sont créés lorsque le potentiel possède un minimum brisant spontanément la symétrie U(1). En 3+1 dimensions, ces vortex deviennent des défauts à une dimension. Ils ap- paraissent par exemple en matière condensée dans les supraconducteurs de type II comme des lignes de flux magnétique. J’analyserai comment l’énergie des solutions statiques dépend des paramètres du modèle et en particulier du nombre d’enroulement du vortex. Pour le choix habituel de potentiel (un poly- nôme quartique dit « BPS »), la relation entre les masses des deux champs mène à deux types de comportements : type I si la masse du champ de jauge est plus grande que celle du champ sca- laire et type II inversement. Selon le cas, la dépendance de l’énergie au nombre d’enroulement, n, indiquera si les vortex auront tendance à s’attirer ou à se repousser, respectivement. Lorsque le flux emprisonné est grand, les vortex présentent un profil où la paroi est mince, permettant certaines simplifications dans l’analyse. Le potentiel, un polynôme d’ordre six (« non-BPS »), est choisi tel que le centre du vortex se trouve dans le vrai vide (minimum absolu du potentiel) alors qu’à l’infini le champ scalaire se retrouve dans le faux vide (minimum relatif du potentiel). Le taux de désintégration a déjà été estimé par une approximation semi-classique pour montrer l’impact des défauts topologiques sur la stabilité du faux vide. Le projet consiste d’abord à établir l’existence de vortex classi- quement stables de façon numérique. Puis, ma contribution fut une analyse des paramètres du modèle révélant le comportement énergétique de ceux-ci en fonction du nombre d’enroulement. Ce comportement s’avèrera être différent du cas « BPS » : le ratio des masses ne réussit pas à décrire le comportement observé numériquement.

THE VORONOI TESSELLATION CLUSTER FINDER IN 2+1 DIMENSIONS

We present a detailed description of the Voronoi Tessellation (VT) cluster finder algorithm in 2+1 dimensions, which improves on past implementations of this technique. The need for cluster finder algorithms able to produce reliable cluster catalogs up to redshift 1 or beyond and down to 10(13.5) solar masses is paramount especially in light of upcoming surveys aiming at cosmological constraints from galaxy cluster number counts. We build the VT in photometric redshift shells and use the two-point correlation function of the galaxies in the field to both determine the density threshold for detection of cluster candidates and to establish their significance. This allows us to detect clusters in a self-consistent way without any assumptions about their astrophysical properties. We apply the VT to mock catalogs which extend to redshift 1.4 reproducing the ACDM cosmology and the clustering properties observed in the Sloan Digital Sky Survey data. An objective estimate of the cluster selection function in terms of the completeness and purity as a function of mass and redshift is as important as having a reliable cluster finder. We measure these quantities by matching the VT cluster catalog with the mock truth table. We show that the VT can produce a cluster catalog with completeness and purity > 80% for the redshift range up to similar to 1 and mass range down to similar to 10(13.5) solar masses.

Ghost free dual vector theories in 2+1 dimensions

We explore here the issue of duality versus spectrum equivalence in dual theories generated through the master action approach. Specifically we examine a generalized self-dual (GSD) model where a Maxwell term is added to the self-dual model. A gauge embedding procedure applied to the GSD model leads to a Maxwell-Chern-Simons (MCS) theory with higher derivatives. We show here that the latter contains a ghost mode contrary to the original GSD model. By figuring out the origin of the ghost we are able to suggest a new master action which interpolates between the local GSD model and a nonlocal MCS model. Those models share the same spectrum and are ghost free. Furthermore, there is a dual map between both theories at classical level which survives quantum correlation functions up to contact terms. The remarks made here may be relevant for other applications of the master action approach.

Duality of parity doublets of helicity +/- 2 in D=2+1 dimensions

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Unitarity of spin-2 theories with linearized Weyl symmetry in D=2+1 dimensions

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Infrared dynamics in (2+1) dimensions

In this work we study the asymptotic behavior of (2+1)-dimensional quantum electrodynamics in the infrared region. We show that an appropriate redefinition of the fermion current operator leads to an asymptotic evolution operator that contains a divergent Coulomb phase factor and a contribution from the electromagnetic field at large distances, factored from the evolution operator for free fields, and we conclude that the modified scattering operator maps two spaces of coherent states of the electromagnetic field, as in the Kulish-Faddeev model for QED (quantum electrodynamics) in four space-time dimensions.

Quadratic gravity theories in 2+1 dimensions and the topological Chern-Simons term

The addition of a topological Chern-Simons term to three-dimensional higher-derivative gravity is not a good therapy to cure the nonunitarity of the aforementioned theory. Moreover, R+R-2 gravity in (2+1)D, which is unitary at the tree level, becomes tree-level nonunitary when it is augmented by the abovementioned topological term. Therefore, unlike what is claimed in the literature, topological higher-derivative gravity in (2+1)D is not tree-level unitary and neither is topological three-dimensional R+R-2 gravity.

Gravity, antigravity and gravitational shielding in (2+1) dimensions

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Effective action for QED in 2+1 dimensions at finite temperature

Both the parity-breaking and parity-invariant parts of the effective action for the gauge field in QED 3 with massive fermions at finite temperature are obtained exactly. This is feasible because we use a particular configuration of the background gauge field, namely a constant magnetic field and a time-dependent time component of the background gauge field. Our results allow us to compute exactly physically interesting quantities such as the induced charge density and fermion condensate whose dependence on the temperature, fermion mass and gauge field is discussed. ©1999 The American Physical Society.

Ghost free dual vector theories in 2 + 1 dimensions

We explore here the issue of duality versus spectrum equivalence in dual theories generated through the master action approach. Specifically we examine a generalized self-dual (GSD) model where a Maxwell term is added to the self-dual model. A gauge embedding procedure applied to the GSD model leads to a Maxwell-Chern-Simons (MCS) theory with higher derivatives. We show here that the latter contains a ghost mode contrary to the original GSD model. By figuring out the origin of the ghost we are able to suggest a new master action which interpolates between the local GSD model and a nonlocal MCS model. Those models share the same spectrum and are ghost free. Furthermore, there is a dual map between both theories at classical level which survives quantum correlation functions up to contact terms. The remarks made here may be relevant for other applications of the master action approach. © SISSA 2006.

Lump solitons in a higher-order nonlinear equation in 2+1 dimensions

We propose and examine an integrable system of nonlinear equations that generalizes the nonlinear Schrodinger equation to 2 + 1 dimensions. This integrable system of equations is a promising starting point to elaborate more accurate models in nonlinear optics and molecular systems within the continuum limit. The Lax pair for the system is derived after applying the singular manifold method. We also present an iterative procedure to construct the solutions from a seed solution. Solutions with one-, two-, and three-lump solitons are thoroughly discussed.

Higher-derivative theory of (2+1)-dimensional gravity

Higher-derivative gravity in 2 + 1 dimensions is considered. The general solution of the linearized field equations in a three-dimensional version of the Teyssandier gauge is obtained, and from that the solution for a static pointlike source is found. The deflection of light rays is also analysed. (C) 2001 Elsevier B.V. B.V. All rights reserved.

Quantization of (2+1)-spinning particles and bifermionic constraint problem

This work is a natural continuation of our recent study in quantizing relativistic particles. There it was demonstrated that, by applying a consistent quantization scheme to the classical model of a spinless relativistic particle as well as to the Berezin-Marinov model of a 3 + 1 Dirac particle, it is possible to obtain a consistent relativistic quantum mechanics of such particles. In the present paper, we apply a similar approach to the problem of quantizing the massive 2 + 1 Dirac particle. However, we stress that such a problem differs in a nontrivial way from the one in 3 + 1 dimensions. The point is that in 2 + 1 dimensions each spin polarization describes different fermion species. Technically this fact manifests itself through the presence of a bifermionic constant and of a bifermionic first-class constraint. In particular, this constraint does not admit a conjugate gauge condition at the classical level. The quantization problem in 2 + 1 dimensions is also interesting from the physical viewpoint (e.g., anyons). In order to quantize the model, we first derive a classical formulation in an effective phase space, restricted by constraints and gauges. Then the condition of preservation of the classical symmetries allows us to realize the operator algebra in an unambiguous way and construct an appropriate Hilbert space. The physical sector of the constructed quantum mechanics contains spin-1/2 particles and antiparticles without an infinite number of negative-energy levels, and exactly reproduces the one-particle sector of the 2 + 1 quantum theory of a spinor field.