Quantum gauge boson propagators in the light front

Gauge fields in the light front are traditionally addressed via, the employment of an algebraic condition n·A = 0 in the Lagrangian density, where Aμ is the gauge field (Abelian or non-Abelian) and nμ is the external, light-like, constant vector which defines the gauge proper. However, this condition though necessary is not sufficient to fix the gauge completely; there still remains a residual gauge freedom that must be addressed appropriately. To do this, we need to define the condition (n·A) (∂·A) = 0 with n·A = 0 = ∂·A. The implementation of this condition in the theory gives rise to a gauge boson propagator (in momentum space) leading to conspicuous nonlocal singularities of the type (k·n)-α where α = 1, 2. These singularities must be conveniently treated, and by convenient we mean not only mathemathically well-defined but physically sound and meaningful as well. In calculating such a propagator for one and two noncovariant gauge bosons those singularities demand from the outset the use of a prescription such as the Mandelstam-Leibbrandt (ML) one. We show that the implementation of the ML prescription does not remove certain pathologies associated with zero modes. However we present a causal, singularity-softening prescription and show how to keep causality from being broken without the zero mode nuisance and letting only the propagation of physical degrees of freedom.

A gauge theory for continuous spin particles

In this dissertation we explore the features of a Gauge Field Theory formulation for continuous spin particles (CSP). To make our discussion as self-contained as possible, we begin by introducing all the basics of Group Theory - and representation theory - which are necessary to understand where the CSP come from. We then apply what we learn from Group Theory to the study of the Lorentz and Poincaré groups, to the point where we are able to construct the CSP representation. Finally, after a brief review of the Higher-Spin formalism, through the Schwinger-Fronsdal actions, we enter the realm of CSP Field Theory. We study and explore all the local symmetries of the CSP action, as well as all of the nuances associated with the introduction of an enlarged spacetime, which is used to formulate the CSP action. We end our discussion by showing that the physical contents of the CSP action are precisely what we expected them to be, in comparison to our Group Theoretical approach.

Perturbative Ward identities for Yang-Mills field theory stochastically quantized

%'e compute the divergent part of the three-point vertex function of the non-Abelian Yang-Mills gauge field theory within the stochastic quantization approach to the one-loop order. This calculation allows us to find four renormalization constants which, together with the four previously obtained, verify, to the calculated order, some Ward identities.

Aspects of a noncommutative scalar/tensor duality

We study the noncommutative massless Kalb-Ramond gauge field coupled to a dynamical U(1) gauge field in the adjoint representation together with a compensating vector field. We derive the Seiberg-Witten map and obtain the corresponding mapped action to first order in theta. The (emergent) gravity structure found in other situations is not present here. The off-shell dual scalar theory is derived and it does not coincide with the Seiberg-Witten mapped scalar theory. Dispersion relations are also discussed. The p-form generalization of the Seiberg-Witten map to order theta is also derived.

Classical noncommutative electrodynamics with external source

In a U(1)(*)-noncommutative gauge field theory we extend the Seiberg-Witten map to include the (gauge-invariance-violating) external current and formulate-to the first order in the noncommutative parameter-gauge-covariant classical field equations. We find solutions to these equations in the vacuum and in an external magnetic field, when the 4-current is a static electric charge of a finite size a, restricted from below by the elementary length. We impose extra boundary conditions, which we use to rule out all singularities, 1/r included, from the solutions. The static charge proves to be a magnetic dipole, with its magnetic moment being inversely proportional to its size a. The external magnetic field modifies the long-range Coulomb field and some electromagnetic form factors. We also analyze the ambiguity in the Seiberg-Witten map and show that at least to the order studied here it is equivalent to the ambiguity of adding a homogeneous solution to the current-conservation equation.

N=1 SQCD-like theories with N_f massive flavors from AdS/CFT and beta functions

We study new supergravity solutions related to large-N c N=1 supersymmetric gauge field theories with a large number N f of massive flavors. We use a recently proposed framework based on configurations with N c color D5 branes and a distribution of N f flavor D5 branes, governed by a function N f S(r). Although the system admits many solutions, under plausible physical assumptions the relevant solution is uniquely determined for each value of x ≡ N f /N c . In the IR region, the solution smoothly approaches the deformed Maldacena-Núñez solution. In the UV region it approaches a linear dilaton solution. For x < 2 the gauge coupling β g function computed holographically is negative definite, in the UV approaching the NSVZ β function with anomalous dimension γ 0 = −1/2 (approaching − 3/(32π 2)(2N c  − N f )g 3)), and with β g  → −∞ in the IR. For x = 2, β g has a UV fixed point at strong coupling, suggesting the existence of an IR fixed point at a lower value of the coupling. We argue that the solutions with x > 2 describe a"Seiberg dual" picture where N f  − 2N c flips sign.

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.

Elétrons fortemente correlacionados na vizinhança de uma transição de fase quântica

The aim of this work is to derive theWard Identity for the low energy effective theory of a fermionic system in the presence of a hyperbolic Fermi surface coupled with a U(1) gauge field in 2+1 dimensions. These identities are important because they establish requirements for the theory to be gauge invariant. We will see that the identity associated Ward Identity (WI) of the model is not preserved at 1-loop order. This feature signalizes the presence of a quantum anomaly. In other words, a classical symmetry is broken dynamically by quantum fluctuations. Furthermore, we are considering that the system is close to a Quantum Phase Transitions and in vicinity of a Quantum Critical Point the fermionic excitations near the Fermi surface, decay through a Landau damping mechanism. All this ingredients need to be take explicitly to account and this leads us to calculate the vertex corrections as well as self energies effects, which in this way lead to one particle propagators which have a non-trivial frequency dependence

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.

Generalized duality between local vector theories in D=2+1

The existence of an interpolating master action does not guarantee the same spectrum for the interpolated dual theories. In the specific case of a generalized self-dual (GSD) model defined as the addition of the Maxwell term to the self-dual model in D = 2 + 1, previous master actions have furnished a dual gauge theory which is either nonlocal or contains a ghost mode. Here we show that by reducing the Maxwell term to first order by means of an auxiliary field we are able to define a master action which interpolates between the GSD model and a couple of non-interacting Maxwell-Chern-Simons theories of opposite helicities. The presence of an auxiliary field explains the doubling of fields in the dual gauge theory. A generalized duality transformation is defined and both models can be interpreted as self-dual models. Furthermore, it is shown how to obtain the gauge invariant correlators of the non-interacting MCS theories from the correlators of the self-dual field in the GSD model and vice-versa. The derivation of the non-interacting MCS theories from the GSD model, as presented here, works in the opposite direction of the soldering approach.

A new spin-2 self-dual model in D=2+1

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Galilean covariant Lagrangian models

We construct non-relativistic Lagrangian field models by enforcing Galilean covariance with a (4, 1) Minkowski manifold followed by a projection onto the (3, 1) Newtonian spacetime. We discuss scalar, Fermi and gauge fields, as well as interactions between these fields, preparing the stage for their quantization. We show that the Galilean covariant formalism provides an elegant construction of the Lagrangians which describe the electric and magnetic limits of Galilean electromagnetism. Similarly we obtain non-relativistic limits for the Proca field. Then we study Dirac Lagrangians and retrieve the Levy-Leblond wave equations when the Fermi field interacts with an Abelian gauge field.

Infrared degrees of freedom of Yang-Mills theory in the Schrodinger representation

We set up a new calculational framework for the Yang-Mills vacuum transition amplitude in the Schrodinger representation. After integrating out hard-mode contributions perturbatively and performing a gauge-invariant gradient expansion of the ensuing soft-mode action, a manageable saddle-point expansion for the vacuum overlap can be formulated. In combination with the squeezed approximation to the vacuum wave functional this allows for an essentially analytical treatment of physical amplitudes. Moreover, it leads to the identification of dominant and gauge-invariant classes of gauge field orbits which play the role of gluonic infrared (IR) degrees of freedom. The latter emerge as a diverse set of saddle-point solutions and are represented by unitary matrix fields. We discuss their scale stability, the associated virial theorem and other general properties including topological quantum numbers and action bounds. We then find important saddle-point solutions (most of them solitons) explicitly and examine their physical impact. While some are related to tunneling solutions of the classical Yang-Mills equation, i.e. to instantons and merons, others appear to play unprecedented roles. A remarkable new class of IR degrees of freedom consists of Faddeev-Niemi type link and knot solutions, potentially related to glueballs.

Renormalized new solutions for the massless Thirring model

We present a nonperturbative study of the (1 + 1)-dimensional massless Thirring model by using path integral methods. The regularization ambiguities - coming from the computation of the fermionic determinant - allow to find new solution types for the model. At quantum level the Ward identity for the 1PI 2-point function for the fermionic current separates such solutions in two phases or sectors, the first one has a local gauge symmetry that is implemented at quantum level and the other one without this symmetry. The symmetric phase is a new solution which is unrelated to the previous studies of the model and, in the nonsymmetric phase there are solutions that for some values of the ambiguity parameter are related to well-known solutions of the model. We construct the Schwinger-Dyson equations and the Ward identities. We make a detailed analysis of their UV divergence structure and, after, we perform a nonperturbative regularization and renormalization of the model.

Manifestly covariant actions for D=4 self-dual Yang-Mills and D=10 super-Yang-Mills

Using an infinite number of fields, we construct actions for D = 4 self-dual Yang-Mills with manifest Lorentz invariance and for D = 10 super-Yang-Mills with manifest super-Poincare invariance. These actions are generalizations of the covariant action for the D = 2 chiral boson which was first studied by McClain, Wu, Yu and Wotzasek.