Overlap for 2D chiral U(1) models

The overlap formulation is applied to an anomaly free combination of chiral fermions coupled to U(1) gauge fields on a 2D torus. Evidence is presented that gauge averaging the overlap phases in these models produces correct continuum results.Comment: 3 pages; uufile contains the tex file, espcrc2.sty file and three ps files; Talk presented in Lattice 96 at St. Louis (Chiral Gauge Theories

Domain Wall Fermions and Chiral Symmetry Restoration Rate

Domain Wall Fermions utilize an extra space time dimension to provide a method for restoring the regularization induced chiral symmetry breaking in lattice vector gauge theories even at finite lattice spacing. The breaking is restored at an exponential rate as the size of the extra dimension increases. As a precursor to lattice QCD studies the dependence of the restoration rate to the other parameters of the theory and, in particular, the lattice spacing is investigated in the context of the two flavor lattice Schwinger model.Comment: 3 pages, LaTex, 5 ps figures, contribution to LATTICE97 proceeding

Domain Wall Fermions and MC Simulations of Vector Theories

It is known that domain wall fermions may be used in MC simulations of vector theories. The practicality and usefulness of such an implementation is investigated in the context of the vector Schwinger model, on a 2+1 dimensional lattice. Preliminary results of a Hybrid Monte Carlo simulation are presented.Comment: Talk presented at LATTICE96(chirality in qcd), 3 pages in LaTex, 4 Postscript figure

Gribov Copy and Complex Phase of Chiral Determinant

We calculate the complex phase of chiral determinant by the vacuum overlap formula with configurations of two-dimensional U(1) gauge field fixed in Landau and Laplacian gauge. The complex phase fluctuates over the Gribov copies, which appear in the process of Landau gauge fixing and contain vortex-like singularities. In the Laplacian gauge, the fluctuation can be reduced and the phase can be determined uniquely. If it is used as a preconditioning for Landau gauge fixing, the most smooth configuration is obtained among the copies generated.Comment: Talk presented at LATTICE96(chiral gauge), 3 LaTeX pages with 5 postscript figures, need espcrc2.sty(included

Formulation of chiral gauge theories

We present a formulation of chiral gauge theories, which admits more general spectra of Dirac operators and reveals considerably more possibilities for the structure of the chiral projections. Our two forms of correlation functions both also apply in the presence of zero modes and for any value of the index. The decomposition of the total set of pairs of bases into equivalence classes is carefully analyzed. Transformation properties are derived.Comment: 3 pages, Lattice2004(chiral

Anomaly free U(1) chiral gauge theories on a two dimensional torus

We consider anomaly free combinations of chiral fermions coupled to $U(1)$ gauge fields on a 2D torus first in the continuum and then on the lattice in the overlap formulation. Both in the continuum and on the lattice, when the background consists of sufficiently large constant gauge potentials the action induced by the fermions varies significantly under certain singular gauge transformations. ``Ruling away'' such discontinuities cannot be justified in the continuum framework and does not naturally fit on the lattice. Complete gauge invariance in the continuum can be restored in some models by choosing special boundary conditions for the fermions. Evidence is presented that gauge averaging the overlap phases in these models produces correct continuum results.Comment: 30 page

Finite size corrections in two dimensional gauge theories and a quantitative chiral test of the overlap

An argument is presented for a certain universality of finite size corrections in two dimensional gauge theories. In the abelian case a direct calculation is carried out for a particular chiral model. The analytical result confirms the above universality and that the 't Hooft vertex previously measured using the overlap smoothly approaches the correct continuum limit within statistical errors.Comment: 11 pages, 1 figure, TeX, eps