Renormalization of lattice gauge theories with massless Ginsparg Wilson fermions

Using functional techniques, we prove, to all orders of perturbation theory, that lattice vector gauge theories with Ginsparg Wilson fermions are renormalizable. For two or more massless fermions, they satisfy a flavour mixing axial vector Ward identity. It involves a lattice specific part that is quadratic in the vertex functional and classically irrelevant. We show that it stays irrelevant under renormalization. This means that in the continuum limit the (standard) chiral symmetry becomes restored. In particular, the flavour mixing current does not require renormalization.Comment: 13 pages, Latex2

Practical Algebraic Renormalization

A practical approach is presented which allows the use of a non-invariant regularization scheme for the computation of quantum corrections in perturbative quantum field theory. The theoretical control of algebraic renormalization over non-invariant counterterms is translated into a practical computational method. We provide a detailed introduction into the handling of the Slavnov-Taylor and Ward-Takahashi identities in the Standard Model both in the conventional and the background gauge. Explicit examples for their practical derivation are presented. After a brief introduction into the Quantum Action Principle the conventional algebraic method which allows for the restoration of the functional identities is discussed. The main point of our approach is the optimization of this procedure which results in an enormous reduction of the calculational effort. The counterterms which have to be computed are universal in the sense that they are independent of the regularization scheme. The method is explicitly illustrated for two processes of phenomenological interest: QCD corrections to the decay of the Higgs boson into two photons and two-loop electroweak corrections to the process $B \to X_s \gamma$.Comment: version to be published in Annals of Physic

Stability and renormalization of Yang-Mills theory with Background Field Method: a regularization independent proof

In this paper the stability and the renormalizability of Yang-Mills theory in the Background Field Gauge are studied. By means of Ward Identities of Background gauge invariance and Slavnov-Taylor Identities the stability of the classical model is proved and, in a regularization independent way, its renormalizability is verified. A prescription on how to build the counterterms is given and the possible anomalies which may appear for Ward Identities and for Slavnov-Taylor Identities are shown.Comment: 25 pages, Latex 2.09, no figure

The Abelian Antighost Equation for The Standard Model in the `t Hooft-Background Gauge

In this paper we study the Abelian Anti-ghost equation for the Standard Model quantized in the 't Hooft-Background gauge. We show that this equation assures the non-renormalization of the abelian ghost fields and prevents possible abelian anomalies.Comment: Latex2e, 22 pages, no figures, use package amssym

Dynamical Breakdown of Symmetry in a (2+1) Dimensional Model Containing the Chern-Simons Field

We study the vacuum stability of a model of massless scalar and fermionic fields minimally coupled to a Chern-Simons field. The classical Lagrangian only involves dimensionless parameters, and the model can be thought as a (2+1) dimensional analog of the Coleman-Weinberg model. By calculating the effective potential, we show that dynamical symmetry breakdown occurs in the two-loop approximation. The vacuum becomes asymmetric and mass generation, for the boson and fermion fields takes place. Renormalization group arguments are used to clarify some aspects of the solution.Comment: Minor modifications in the text and figure

On a class of embeddings of massive Yang-Mills theory

A power-counting renormalizable model into which massive Yang-Mills theory is embedded is analyzed. The model is invariant under a nilpotent BRST differential s. The physical observables of the embedding theory, defined by the cohomology classes of s in the Faddeev-Popov neutral sector, are given by local gauge-invariant quantities constructed only from the field strength and its covariant derivatives.Comment: LATEX, 34 pages. One reference added. Version published in the journa

The Lattice Schwinger Model: Confinement, Anomalies, Chiral Fermions and All That

In order to better understand what to expect from numerical CORE computations for two-dimensional massless QED (the Schwinger model) we wish to obtain some analytic control over the approach to the continuum limit for various choices of fermion derivative. To this end we study the Hamiltonian formulation of the lattice Schwinger model (i.e., the theory defined on the spatial lattice with continuous time) in $A_0=0$ gauge. We begin with a discussion of the solution of the Hamilton equations of motion in the continuum, we then parallel the derivation of the continuum solution within the lattice framework for a range of fermion derivatives. The equations of motion for the Fourier transform of the lattice charge density operator show explicitly why it is a regulated version of this operator which corresponds to the point-split operator of the continuum theory and the sense in which the regulated lattice operator can be treated as a Bose field. The same formulas explicitly exhibit operators whose matrix elements measure the lack of approach to the continuum physics. We show that both chirality violating Wilson-type and chirality preserving SLAC-type derivatives correctly reproduce the continuum theory and show that there is a clear connection between the strong and weak coupling limits of a theory based upon a generalized SLAC-type derivative.Comment: 27 pages, 3 figures, revte

Higher-order non-symmetric counterterms in pure Yang-Mills theory

We analyze the restoration of the Slavnov-Taylor (ST) identities for pure massless Yang-Mills theory in the Landau gauge within the BPHZL renormalization scheme with IR regulator. We obtain the most general form of the action-like part of the symmetric regularized action, obeying the relevant ST identities and all other relevant symmetries of the model, to all orders in the loop expansion. We also give a cohomological characterization of the fulfillment of BPHZL IR power-counting criterion, guaranteeing the existence of the limit where the IR regulator goes to zero. The technique analyzed in this paper is needed in the study of the restoration of the ST identities for those models, like the MSSM, where massless particles are present and no invariant regularization scheme is known to preserve the full set of ST identities of the theory.Comment: Final version published in the journa

Six-body Light-Front Tamm-Dancoff approximation and wave functions for the massive Schwinger model

The spectrum of the massive Schwinger model in the strong coupling region is obtained by using the light-front Tamm-Dancoff (LFTD) approximation up to including six-body states. We numerically confirm that the two-meson bound state has a negligibly small six-body component. Emphasis is on the usefulness of the information about states (wave functions). It is used for identifying the three-meson bound state among the states below the three-meson threshold. We also show that the two-meson bound state is well described by the wave function of the relative motion.Comment: 19 pages, RevTeX, 7 figures are available upon request; Minor errors have been corrected; Final version to appear in Phys.Rev.

On the trace identity in a model with broken symmetry

Considering the simple chiral fermion meson model when the chiral symmetry is explicitly broken, we show the validity of a trace identity -- to all orders of perturbation theory -- playing the role of a Callan-Symanzik equation and which allows us to identify directly the breaking of dilatations with the trace of the energy-momentum tensor. More precisely, by coupling the quantum field theory considered to a classical curved space background, represented by the non-propagating external vielbein field, we can express the conservation of the energy-momentum tensor through the Ward identity which characterizes the invariance of the theory under the diffeomorphisms. Our ``Callan-Symanzik equation'' then is the anomalous Ward identity for the trace of the energy-momentum tensor, the so-called ``trace identity''.Comment: 11 pages, Revtex file, final version to appear in Phys.Rev.