SPECTRUM OF SCREENING MASSES FOR SU(2) GAUGE THEORY: UNIVERSALITY CLASS

In this work we study the spectrum of the lowest screening masses for Yang-Mills theories on the lattice. We used the SU(2) gauge group in (3 + 1) dmensions. We adopted the multiple exponential method and the so-called ""variational"" method, in order to detect possible excited states. The calculations were done near the critical temperature of the confinement-deconfinement phase transition. We obtained values for the ratios of the screening masses consistent with predictions from universality arguments. A Monte Carlo evolution of the screening masses in the gauge theory confirms the validity of the predictions.

On the generalized eigenvalue method for energies and matrix elements in lattice field theory

We discuss the generalized eigenvalue problem for computing energies and matrix elements in lattice gauge theory, including effective theories such as HQET. It is analyzed how the extracted effective energies and matrix elements converge when the time separations are made large. This suggests a particularly efficient application of the method for which we can prove that corrections vanish asymptotically as exp(-(E(N+1) - E(n))t). The gap E(N+1) - E(n) can be made large by increasing the number N of interpolating fields in the correlation matrix. We also show how excited state matrix elements can be extracted such that contaminations from all other states disappear exponentially in time. As a demonstration we present numerical results for the extraction of ground state and excited B-meson masses and decay constants in static approximation and to order 1/m(b) in HQET.

Pseudoclassical description of scalar particle in non-abelian background and path-integral representations

Path-integral representations for a scalar particle propagator in non-Abelian external backgrounds are derived. To this aim, we generalize the procedure proposed by Gitman and Schvartsman of path-integral construction to any representation of SU(N) given in terms of antisymmetric generators. And for arbitrary representations of SU(N), we present an alternative construction by means of fermionic coherent states. From the path-integral representations we derive pseudoclassical actions for a scalar particle placed in non-Abelian backgrounds. These actions are classically analyzed and then quantized to prove their consistency.

Self-dual hopfions

We construct static and time-dependent exact soliton solutions with nontrivial Hopf topological charge for a field theory in 3 + 1 dimensions with the target space being the two dimensional sphere S(2). The model considered is a reduction of the so-called extended Skyrme-Faddeev theory by the removal of the quadratic term in derivatives of the fields. The solutions are constructed using an ansatz based on the conformal and target space symmetries. The solutions are said self-dual because they solve first order differential equations which together with some conditions on the coupling constants, imply the second order equations of motion. The solutions belong to a sub-sector of the theory with an infinite number of local conserved currents. The equation for the profile function of the ansatz corresponds to the Bogomolny equation for the sine-Gordon model.

Static Hopfions in the extended Skyrme-Faddeev model

We construct static soliton solutions with non-zero Hopf topological charges to a theory which is an extension of the Skyrme-Faddeev model by the addition of a further quartic term in derivatives. We use an axially symmetric ansatz based on toroidal coordinates, and solve the resulting two coupled non-linear partial differential equations in two variables by a successive over-relaxation (SOR) method. We construct numerical solutions with Hopf charge up to four, and calculate their analytical behavior in some limiting cases. The solutions present an interesting behavior under the changes of a special combination of the coupling constants of the quartic terms. Their energies and sizes tend to zero as that combination approaches a particular special value. We calculate the equivalent of the Vakulenko and Kapitanskii energy bound for the theory and find that it vanishes at that same special value of the coupling constants. In addition, the model presents an integrable sector with an in finite number of local conserved currents which apparently are not related to symmetries of the action. In the intersection of those two special sectors the theory possesses exact vortex solutions (static and time dependent) which were constructed in a previous paper by one of the authors. It is believed that such model describes some aspects of the low energy limit of the pure SU(2) Yang-Mills theory, and our results may be important in identifying important structures in that strong coupling regime.

Exact vortex solutions in an extended Skyrme-Faddeev model

We construct exact vortex solutions in 3+1 dimensions to a theory which is an extension, due to Gies, of the Skyrme-Faddeev model, and that is believed to describe some aspects of the low energy limit of the pure SU(2) Yang-Mills theory. Despite the efforts in the last decades those are the first exact analytical solutions to be constructed for such type of theory. The exact vortices appear in a very particular sector of the theory characterized by special values of the coupling constants, and by a constraint that leads to an infinite number of conserved charges. The theory is scale invariant in that sector, and the solutions satisfy Bogomolny type equations. The energy of the static vortex is proportional to its topological charge, and waves can travel with the speed of light along them, adding to the energy a term proportional to a U(1) No ether charge they create. We believe such vortices may play a role in the strong coupling regime of the pure SU(2) Yang-Mills theory.

Axially symmetric soliton solutions in a Skyrme-Faddeev-type model with Gies`s extension

We construct static soliton solutions with non-zero Hopf topological charges to a theory which is the extended Skyrme-Faddeev model with a further quartic term in derivatives. We use an axially symmetric ansatz based on toroidal coordinates, and solve the resulting two coupled nonlinear partial differential equations in two variables by a successive over-relaxation method. We construct numerical solutions with the Hopf charge up to 4. The solutions present an interesting behavior under the changes of a special combination of the coupling constants of the quartic terms.

Linear covariant gauges on the lattice

Linear covariant gauges, such as Feynman gauge, are very useful in perturbative calculations. Their non-perturbative formulation is, however, highly non-trivial. In particular, it is a challenge to define linear covariant gauges on a lattice. We consider a class of gauges in lattice gauge theory that coincides with the perturbative definition of linear covariant gauges in the formal continuum limit. The corresponding gauge-fixing procedure is described and analyzed in detail, with an application to the pure SU(2) case. In addition, results for the gluon propagator in the two-dimensional case are given. (C) 2008 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.