Positivity violation for the lattice Landau gluon propagator

We present explicit numerical evidence of reflection-positivity violation for the lattice Landau gluon propagator in three-dimensional pure SU(2) gauge theory. We use data obtained at very large lattice volumes (V = 80(3), 140(3)) and for three different lattice couplings in the scaling region (beta = 4.2, 5.0, 6.0). In particular, we observe a clear oscillatory pattern in the real-space propagator C(t). We also verify that the (real-space) data show good scaling in the range t is an element of[0, 3]fm and can be fitted using a Gribov-like form. The violation of positivity is in contradiction with a stable-particle interpretation of the associated field theory and may be viewed as a manifestation of confinement.

Gravitation without the equivalence principle

In the general relativistic description of gravitation, geometry replaces the concept of force. This is possible because of the universal character of free fall, and would break down in its absence. on the other hand, the teleparallel version of general relativity is a gauge theory for the translation group and, as such, describes the gravitational interaction by a force similar to the Lorentz force of electromagnetism, a non-universal interaction. Relying on this analogy it is shown that, although the geometric description of general relativity necessarily requires the existence of the equivalence principle, the teleparallel gauge approach remains a consistent theory for gravitation in its absence.

Metric-affine approach to teleparallel gravity

The teleparallel gravity theory, treated physically as a gauge theory of translations, naturally represents a particular case of the most general gauge-theoretic model based on the general affine group of spacetime. on the other hand, geometrically, the Weitzenbock spacetime of distant parallelism is a particular case of the general metric-affine spacetime manifold. These physical and geometrical facts offer a new approach to teleparallelism. We present a systematic treatment of teleparallel gravity within the framework of the metric-affine theory. The symmetries, conservation laws and the field equations are consistently derived, and the physical consequences are discussed in detail. We demonstrate that the so-called teleparallel GR-equivalent model has a number of attractive features which distinguishes it among the general teleparallel theories, although it has a consistency problem when dealing with spinning matter sources.

Temporal correlator in YM32 and reflection-positivity violation

We consider numerical data for the lattice Landau gluon propagator obtained at very large lattice volumes in three-dimensional pure SU(2) Yang-Mills gauge theory (YM32). We find that the temporal correlator C(t) shows an oscillatory pattern and is negative for several values of t. This is an explicit violation of reflection positivity and can be related to gluon confinement. We also obtain a good fit for this quantity in the whole time interval using a sum of Stingl-like propagators.

INVESTIGATIONS IN THE LEE-WICK ELECTRODYNAMICS

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Light composite Higgs from an effective action for technicolor

We compute an effective action for a composite Higgs boson formed by new fermions belonging to a general technicolor non-Abelian gauge theory, using a quite general expression for the fermionic self-energy that depends on a certain parameter (alpha), that defines the technicolor theory from the extreme walking behavior up to the one with a standard operator product expansion behavior. We discuss the values of the trilinear and quadrilinear scalar couplings. Our calculation spans all the possible physical possibilities for mass and couplings of the composite system. In the case of extreme walking technicolor theories we verify that it is possible to have a composite Higgs boson with a mass as light as the present experimental limit, contrary to the usual expectation of a heavy mass for the composite Higgs boson. In this case we obtain an upper limit for the Higgs boson mass, (M(H)<= O(700) GeV for SU(2)(TC)), and the experimental data on the Higgs boson mass constrain SU(N)(TC) technicolor gauge groups to be smaller than SU(10)(TC).

5D Yang-Mills instantons from Aharony-Bergman-Jafferis-Maldacena monopoles

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Selected topics in teleparallel gravity

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

BFFT formalism applied to the minimal chiral Schwinger model

We consider the minimal chiral Schwinger model, by embedding the gauge non-invariant formulation into a gauge theory following the Batalin-Fradkin-Fradkina-Tyutin point of view. Within the BFFT procedure, the second-class constraints are converted into strongly involutive first-class ones, leading to an extended gauge-invariant formulation. We also show that, like the standard chiral model, in the minimal chiral model the Wess-Zumino action can be obtained by performing a q-number gauge transformation into the effective gauge non-invariant action.

The SU(2) Skyrme model and anomaly

The SU(2) Shyrme model, expanding in the collective coordinates variables, gives rise to second-class constraints. Recently this system was embedded in a more general Abelian gauge theory using the BFFT Hamiltonian method. in this work we quantize this gauge theory computing the Noether current anomaly using for this two different methods: an operatorial Dirac first class formalism and the non-local BV quantization coupled with the Fujikawa regularization procedure. (C) 2000 Elsevier B.V. B.V. All rights reserved.

Gravitational Lorentz force and the description of the gravitational interaction

In the context of a gauge theory for the translation group, we have obtained, for a spinless particle, a gravitational analogue of the Lorentz force. Then, we have shown that this force equation can be rewritten in terms of magnitudes related to either the teleparallel or the Riemannian structures induced in spacetime by the presence of the gravitational field. In the first case, it gives a force equation, with torsion playing the role of force. In the second, it gives the usual geodesic equation of general relativity. The main conclusion is that scalar matter is able to feel any one of the above spacetime geometries, the teleparallel and the metric ones. Furthermore, both descriptions are found to be completely equivalent in the sense that they give the same physical trajectory for a spinless particle in a gravitational field.

Symmetry transform in Faddeev-Jackiw quantization of dual models

We study the presence of symmetry transformations in the Faddeev-Jackiw approach for constrained systems. Our analysis is based in the case of a particle submitted to a particular potential which depends on an arbitrary function. The method is implemented in a natural way and symmetry generators are identified. These symmetries permit us to obtain the absent elements of the sympletic matrix which complement the set of Dirac brackets of such a theory. The study developed here is applied in two different dual models. First, we discuss the case of a two-dimensional oscillator interacting with an electromagnetic potential described by a Chern-Simons term and second the Schwarz-Sen gauge theory, in order to obtain the complete set of non-null Dirac brackets and the correspondent Maxwell electromagnetic theory limit. ©1999 The American Physical Society.

Gravitational Energy-Momentum Density in Teleparallel Gravity

In the context of a gauge theory for the translation group, a conserved energy-momentum gauge current for the gravitational field is obtained. It is a true spacetime and gauge tensor, and transforms covariantly under global Lorentz transformations. By rewriting the gauge gravitational field equation in a purely spacetime form, it becomes the teleparallel equivalent of Einstein's equation, and the gauge current reduces to the Møller's canonical energy-momentum density of the gravitational field.

Gauged thirring model in the Heisenberg picture

We consider the (2+1)-dimensional gauged Thirring model in the Heisenberg picture. In this context we evaluate the vacuum polarization tensor as well as the corrected gauge boson propagator and address the issues of generation of mass and dynamics for the gauge boson (in the limits of QED 3 and Thirring model as a gauge theory, respectively) due to the radiative corrections.

Multicharged dyonic integrable models

We introduce and study new integrable models (IMs) of An (1)-nonabelian Toda type which admit U(1) ⊗ U(1) charged topological solitons. They correspond to the symmetry breaking SU(n + 1) → SU(2) ⊗ SU(2) ⊗ U(1)n-2 and are conjectured to describe charged dyonic domain walls of N = 1 SU(n + 1) SUSY gauge theory in large n limit. It is shown that this family of relativistic IMs corresponds to the first negative grade q = -1 member of a dyonic hierarchy of generalized cKP type. The explicit relation between the 1-soliton solutions (and the conserved charges as well) of the IMs of grades q = -1 and q = 2 is found. The properties of the IMs corresponding to more general symmetry breaking SU(n + 1) → SU(2)⊗p ⊗ U(1)n-p as well as IM with global SU(2) symmetries are discussed. © 2002 Elsevier Science B.V. All rights reserved.