A note on the practical feasibility of domain-wall fermions

Domain-wall fermions preserve chiral symmetry up to terms that decrease exponentially when the lattice size in the fifth dimension is taken to infinity. The associated rates of convergence are given by the low-lying eigenvalues of a simple local operator in four dimensions. These can be computed using the Ritz functional technique and it turns out that the convergence tends to be extremely slow in the range of lattice spacings relevant to large-volume numerical simulations of lattice QCD. Two methods to improve on this situation are discussed.Comment: 14 pages, talk given by P. H. at the workshop on {\em Current theoretical problems in lattice field theory}, Ringberg, German

Large rescaling of the Higgs condensate: theoretical motivations and lattice results

In the Standard Model the Fermi constant is associated with the vacuum expectation value of the Higgs field, `the condensate', usually believed to be a cutoff-independent quantity. General arguments related to the `triviality' of $\Phi^4$ theory in 4 space-time dimensions suggest, however, a dramatic renormalization effect in the continuum limit that is clearly visible on the relatively large lattices available today. The result can be crucial for the Higgs phenomenology and in any context where spontaneous symmetry breaking is induced through scalar fields.Comment: LATTICE99(Higgs) 3 pages, 3 figure

A perturbative determination of O(a) boundary improvement coefficients for the Schr\"odinger Functional coupling at 1-loop with improved gauge actions

We determine O($a$) boundary improvement coefficients up to 1-loop level for the Schr\"odinger Functional coupling with improved gauge actions including plaquette and rectangle loops. These coefficients are required to implement 1-loop O($a$) improvement in full QCD simulations for the coupling with the improved gauge actions. To this order, lattice artifacts of step scaling function for each improved gauge action are also investigated. In addition, passing through the SF scheme, we estimate the ratio of $\Lambda$-parameters between the improved gauge actions and the plaquette action more accurately.Comment: 17 pages, 2 figures, 6 table

Quark confinement and the bosonic string

Using a new type of simulation algorithm for the standard SU(3) lattice gauge theory that yields results with unprecedented precision, we confirm the presence of a $\gamma/r$ correction to the static quark potential at large distances $r$, with a coefficient $\gamma$ as predicted by the bosonic string theory. In both three and four dimensions, the transition from perturbative to string behaviour is evident from the data and takes place at surprisingly small distances.Comment: TeX source, 21 pages, figures include

Spin-flop transitions and spin-wave gaps in La_2CuO_4

We study the spin-wave spectrum and the spin-flop transitions in La_2CuO_4 in a uniform magnetic field at zero temperature. Using the non-linear sigma-model, we show that a field applied along the orthorhombic b direction leads to a two-step rotation of the staggered magnetization, first in the bc and then in the ac plane, until the order parameter is completely aligned along the c axis. In contrast, for a perpendicular magnetic field, we find a conventional spin-flop transition induced by the competition between the field and the interlayer coupling. A comparison with recent measurements of the field-dependence of the in-plane spin-wave gap shows a beautiful agreement between theory and experiments.Comment: 7 pages, 3 figures; added referenc

The D234 action for light quarks

We investigate a new light fermion action (the ``D234'' action), which is accurate up to \O(a^3) and tadpole-improved \O(a \alpha_s) errors. Using D234 with Symanzik- and tadpole-improved glue we find evidence that continuum results for the quenched hadron spectrum (pion, rho and nucleon) can be obtained on coarse lattices.Comment: Latex, 4 pages, submitted to Lattice '95 proceeding

The gradient flow running coupling with twisted boundary conditions

We study the gradient flow for Yang-Mills theories with twisted boundary conditions. The perturbative behavior of the energy density $\langle E(t)\rangle$ is used to define a running coupling at a scale given by the linear size of the finite volume box. We compute the non-perturbative running of the pure gauge $SU(2)$ coupling constant and conclude that the technique is well suited for further applications due to the relatively mild cutoff effects of the step scaling function and the high numerical precision that can be achieved in lattice simulations. We also comment on the inclusion of matter fields.Comment: 27 pages. LaTe

Perturbative calculation of improvement coefficients to O(g^2a) for bilinear quark operators in lattice QCD

We calculate the O(g^2 a) mixing coefficients of bilinear quark operators in lattice QCD using a standard perturbative evaluation of on-shell Green's functions. Our results for the plaquette gluon action are in agreement with those previously obtained with the Schr\"odinger functional method. The coefficients are also calculated for a class of improved gluon actions having six-link terms.Comment: 14 pages, REVTe

Towards Weyl fermions on the lattice without artefacts

In spite of the breakthrough in non-perturbative chiral gauge theories during the last decade, the present formulation has stubborn artefacts. Independently of the fermion representation one is confronted with unwanted CP violation and infinitely many undetermined weight factors. Renormalization group identifies the culprit. We demonstrate the procedure on Weyl fermions in a real representation

Chiral Lattice Gauge Theories and The Strong Coupling Dynamics of a Yukawa-Higgs Model with Ginsparg-Wilson Fermions

The Yukawa-Higgs/Ginsparg-Wilson-fermion construction of chiral lattice gauge theories described in hep-lat/0605003 uses exact lattice chirality to decouple the massless chiral fermions from a mirror sector, whose strong dynamics is conjectured to give cutoff-scale mass to the mirror fermions without breaking the chiral gauge symmetry. In this paper, we study the mirror sector dynamics of a two-dimensional chiral gauge theory in the limitof strong Yukawa and vanishing gauge couplings, in which case it reduces to an XY model coupled to Ginsparg-Wilson fermions. For the mirror fermions to acquire cutoff-scale mass it is believed to be important that the XY model remain in its "high temperature" phase, where there is no algebraic ordering--a conjecture supported by the results of our work. We use analytic and Monte-Carlo methods with dynamical fermions to study the scalar and fermion susceptibilities, and the mirror fermion spectrum. Our results provide convincing evidence that the strong dynamics does not "break" the chiral symmetry (more precisely, that the mirror fermions do not induce algebraic ordering in two-dimensions), and that the mirror fermions decouple from the infrared physics.Comment: 44 pages, 18 figures; v2: clarification of fermion operators, discussion of recent related work