Chiral symmetry breaking in QCD-like gauge theories with a confining propagator and dynamical gauge boson mass generation

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Structural aspects of the fermion-boson mapping in two-dimensional gauge and anomalous gauge theories with massive fermions

Using a synthesis of the functional integral and operator approaches we discuss the fermion-buson mapping and the role played by the Bose field algebra in the Hilbert space of two-dimensional gauge and anomalous gauge field theories with massive fermions. In QED, with quartic self-interaction among massive fermions, the use of an auxiliary vector field introduces a redundant Bose field algebra that should not be considered as an element of the intrinsic algebraic structure defining the model. In anomalous chiral QED, with massive fermions the effect of the chiral anomaly leads to the appearance in the mass operator of a spurious Bose field combination. This phase factor carries no fermion selection rule and the expected absence of Theta-vacuum in the anomalous model is displayed from the operator solution. Even in the anomalous model with massive Fermi fields, the introduction of the Wess-Zumino field replicates the theory, changing neither its algebraic content nor its physical content. (C) 2002 Elsevier B.V. (USA).

ON THE INDEPENDENT-PARTICLE APPROXIMATION OF GAUGE-THEORIES - A SIMPLE EXAMPLE

In this work the independent particle model formulation is studied as a mean-field approximation of gauge theories using the path integral approach in the framework of quantum electrodynamics in 1 + 1 dimensions. It is shown how a mean-field approximation scheme can be applied to fit an effective potential to an independent particle model, building a straightforward relation between the model and the associated gauge field theory. An example is made considering the problem of massive Dirac fermions on a line, the so called massive Schwinger model. An interesting result is found, indicating a behaviour of screening of the charges in the relativistic limit of strong coupling. A forthcoming application of the method developed to confining potentials in independent quark models for QCD is in view and is briefly discussed.

Extended gauge theories

A scheme inspired in Lie algebra extensions is introduced that enlarges gauge models to allow some coupling between space-time and gauge space. Everything may be written in terms of a generalized covariant derivative including usual differential plus purely algebraic terms. A noncovariant vacuum appears, introducing a natural symmetry breaking, but currents satisfy conservation laws alike those found in gauge theories. © 1991 American Institute of Physics.

Toda lattice field theories, discrete W algebras, Toda lattice hierarchies and quantum groups

In analogy with the Liouville case we study the sl3 Toda theory on the lattice and define the relevant quadratic algebra and out of it we recover the discrete W3 algebra. We define an integrable system with respect to the latter and establish the relation with the Toda lattice hierarchy. We compute the relevant continuum limits. Finally we find the quantum version of the quadratic algebra.

Quartic fermion self-interactions in two-dimensional gauge theories

In this work we discuss the effect of quartic fermion self-interacting terms on the dynamically generated photon masses in 1+1 dimensions, for vector, chiral, and non-Abelian couplings. In the vector and chiral cases we find exactly the dynamically generated mass modified by the quartic term while in the non-Abelian case we find the dynamically generated mass associated with its Abelian part. We show that in the three cases there is a kind of duality between the gauge and quartic couplings. We perform functional as well as operator treatments allowing for the obtention of both fermion and vector field solutions. The structures of the Abelian models in terms of θ vacua are also addressed.

Fixed points and vacuum energy of dynamically broken gauge theories

We show that if a gauge theory with dynamical symmetry breaking has nontrivial fixed points, they will correspond to extrema of the vacuum energy. This relationship provides a different method to determine fixed points.

Quantum topology change and large-N gauge theories

We study a model for dynamical localization of topology using ideas from non-commutative geometry and topology in quantum mechanics. We consider a collection X of N one-dimensional manifolds and the corresponding set of boundary conditions (self-adjoint extensions) of the Dirac operator D. The set of boundary conditions encodes the topology and is parameterized by unitary matrices g. A particular geometry is described by a spectral triple x(g) = (A X, script H sign X, D(g)). We define a partition function for the sum over all g. In this model topology fluctuates but the dimension is kept fixed. We use the spectral principle to obtain an action for the set of boundary conditions. Together with invariance principles the procedure fixes the partition function for fluctuating topologies. The model has one free-parameter β and it is equivalent to a one plaquette gauge theory. We argue that topology becomes localized at β = ∞ for any value of N. Moreover, the system undergoes a third-order phase transition at β = 1 for large-N. We give a topological interpretation of the phase transition by looking how it affects the topology. © SISSA/ISAS 2004.

Connection space approach to ambiguities of gauge theories

Two distinct gauge potentials can have the same field strength, in which case they are said to be copies of each other. The consequences of this ambiguity for the general affine space A of gauge potentials are examined. Any two potentials are connected by a straight line in A, but a straight line going through two copies either contains no other copy or is entirely formed by copies. Copyright © 2005 Hindawi Publishing Corporation.

Chaotic thermalization in classical gauge theories

We explore the idea that chaos concepts might be useful for understanding the thermalization in gauge theories. The SU(2) Higgs model is discussed as a prototype of system with gauge fields coupled to matter fields. Through the numerical solution of the equations of motion, we are able to characterize chaotic behavior via the corresponding Lyapunov exponent. Then it is demonstrated that the system's approach to equilibrium can be understood through direct application of the principles of Statistical Mechanics. © 2013 AIP Publishing LLC.

Study of the ℤ3 symmetry in QCD at finite temperature and chemical potential using a worm algorithm

Traditional Monte Carlo simulations of QCD in the presence of a baryon chemical potential are plagued by the complex phase problem and new numerical approaches are necessary for studying the phase diagram of the theory. In this work we consider a ℤ3 Polyakov loop model for the deconfining phase transition in QCD and discuss how a flux representation of the model in terms of dimer and monomer variable solves the complex action problem. We present results of numerical simulations using a worm algorithm for the specific heat and two-point correlation function of Polyakov loops. Evidences of a first order deconfinement phase transition are discussed. © 2013 American Institute of Physics.

Restrictions over two-dimensional gauge models with Thirring-like interaction

Some years ago, it was shown how fermion self-interacting terms of the Thirring-type impact the usual structure of massless two-dimensional gauge theories [1]. In that work only the cases of pure vector and pure chiral gauge couplings have been considered and the corresponding Thirring term was also pure vector and pure chiral respectively, such that the vector ( or chiral) Schwinger model should not lose its chirality structure due to the addition of the quartic interaction term. Here we extend this analysis to a generalized vector and axial coupling both for the gauge interaction and the quartic fermionic interactions. The idea is to perform quantization without losing the original structure of the gauge coupling. In order to do that we make use of an arbitrariness in the definition of the Thirring-like interaction.

A possible way to relate the covariantization and the negative dimensional integration method in the light-cone gauge

Here we present a possible way to relate the method of covariantizing the gauge-dependent pole and the negative dimensional integration method for computing Feynman integrals pertinent to the light-cone gauge fields. Both techniques are applicable to the algebraic light-cone gauge and dispense with prescriptions to treat the characteristic poles.

Gauge groups from brane-anti-brane systems at angles

We discuss a system formed by two pairs of brane-anti-brane that form an arbitrary angle in a plane. We identify the gauge groups from this system which presumably could be used to construct gauge theories.

Vacuum energy as a c-function for theories with dynamically generated masses

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)