We present a study of the neutron electric dipole moment ( d N ) within the framework of lattice QCD with two flavors of dynamical light quarks. The dipole moment is sensitive to the topological structure of the gauge fields, and accuracy can only be achieved by using dynamical, or sea quark, calculations. However, the topological charge evolves slowly in these calculations, leading to a relatively large uncertainty in d N . It is shown, using quenched configurations, that a better sampling of the charge distribution reduces this problem, but because the CP even part of the fermion determinant is absent, both the topological charge distribution and d N are pathological in the chiral limit. We discuss the statistical and systematic uncertainties arising from the topological charge distribution and unphysical size of the quark mass in our calculations and prospects for eliminating them.Our calculations employ the RBC collaboration two flavor domain wall fermion and DBW2 gauge action lattices with inverse lattice spacing a −1 ≈ 1.7 GeV, physical volume V ≈ (2 fm) 3 , and light quark mass roughly equal to the strange quark mass (m sea = 0.03 and 0.04). We determine a value of the electric dipole moment that is zero within (statistical) errors, | d N | = −0.04(20) e-θ-fm at the smaller sea quark mass. Satisfactory results for the magnetic and electric form factors of the proton and neutron are also obtained and presented.

We reexamine the strong-coupling limit of the Schwinger model on a lattice using staggered fermions and the Hamiltonian approach to lattice gauge theories. Although staggered fermions have no continuous chiral symmetry, they possess a discrete axial invariance that forbids a fermion mass and must be broken in order for the lattice Schwinger model to exhibit the features of the spectrum of the continuum theory. We show that this discrete symmetry is indeed broken spontaneously in the strong-coupling limit. Expanding around a gaugeinvariant ground state and carefully considering the normal ordering of the charge operator, we derive an improved strong-coupling expansion and compute the masses of the low-lying bosonic excitations as well as the chiral condensate of the model. We find very good agreement between our lattice calculations and known continuum values for these quantities already in the fourth order of strong-coupling perturbation theory. We also find the exact ground state of the antiferromagnetic Ising spin chain with the long-range Coulomb interaction, which determines the nature of the ground state in the strong-coupling limit.

We revisit the lattice formulation of the Abelian Chern-Simons model defined on an infinite Euclidean lattice. We point out that any gauge invariant, local and parity odd Abelian quadratic form exhibits, in addition to the zero eigenvalue associated with the gauge invariance and to the physical zero mode at p = 0 due to translational invariance, a set of extra zero eigenvalues inside the Brillouin zone. For the Abelian Chern-Simons theory, which is linear in the derivative, this proliferation of zero modes is reminiscent of the Nielsen-Ninomiya no-go theorem for fermions. A gauge invariant, local and parity even term such as the Maxwell action leads to the elimination of the extra zeros by opening a gap with a mechanism similar to that leading to Wilson fermions on the lattice.

A simulation of quenched QCD with the overlap Dirac operator has been completed using 100 Wilson gauge configurations at β = 6 on an 18 3 × 64 lattice and at β = 5.85 on a 14 3 × 48 lattice, both in Landau gauge. We present results for light meson and baryon masses, meson final state "wave functions," and other observables, as well as some details on the numerical techniques that were used. Our results indicate that scaling violations, if any, are small. We also present an analysis of diquark correlations using the quark propagators generated in our simulation. PACS numbers: 11.15.Ha, 11.30.Rd,.Gc * UMR 6207 du CNRS et des universités d'Aix-Marseille I, II et du Sud Toulon-Var, affiliéeà la FRUMAM.

We introduce a simple method to find localized exact fermionic zero modes for any local fermionic action. The zero modes are attached to specific local gauge configurations. Examples are provided for staggered and Wilson fermion actions in 2-6 dimensions, at finite and infinite lattice volumes, and for abelian and non-abelian gauge groups. One of our concrete results is that a finite density of almost zero modes must occur in quenched four dimensional lattice gauge theory simulations that use traditional methods. This density is exponentially suppressed in the gauge coupling constant.