Remark on lattice BRST invariance

A recently claimed resolution to the lattice Gribov problem in the context of chiral lattice gauge theories is examined. Unfortunately, I find that the old problem remains.Comment: 4 pages, plain TeX, presentation improved (see acknowledgments

Proposal for the numerical solution of planar QCD

Using quenched reduction, we propose a method for the numerical calculation of meson correlation functions in the planar limit of QCD. General features of the approach are outlined, and an example is given in the context of two-dimensional QCD.Comment: 31 pages, 10 figures, uses axodraw.sty, To appear in Physical Review

Two dimensional fermions in three dimensional YM

Dirac fermions in the fundamental representation of SU(N) live on the surface of a cylinder embedded in $R^3$ and interact with a three dimensional SU(N) Yang Mills vector potential preserving a global chiral symmetry at finite $N$. As the circumference of the cylinder is varied from small to large, the chiral symmetry gets spontaneously broken in the infinite $N$ limit at a typical bulk scale. Replacing three dimensional YM by four dimensional YM introduces non-trivial renormalization effects.Comment: 21 pages, 7 figures, 5 table

Spectrum of the Hermitian Wilson-Dirac Operator for a Uniform Magnetic Field in Two Dimensions

It is shown that the eigenvalue problem for the hermitian Wilson-Dirac operator of for a uniform magnetic field in two dimensions can be reduced to one-dimensional problem described by a relativistic analog of the Harper equation. An explicit formula for the secular equations is given in term of a set of polynomials. The spectrum exhibits a fractal structure in the infinite volume limit. An exact result concerning the index theorem for the overlap Dirac operator is obtained.Comment: 8 pages, latex, 3 eps figures, minor correction

A Perturbative Study of a General Class of Lattice Dirac Operators

A perturbative study of a general class of lattice Dirac operators is reported, which is based on an algebraic realization of the Ginsparg-Wilson relation in the form $\gamma_{5}(\gamma_{5}D)+(\gamma_{5}D)\gamma_{5} = 2a^{2k+1}(\gamma_{5}D)^{2k+2}$ where $k$ stands for a non-negative integer. The choice $k=0$ corresponds to the commonly discussed Ginsparg-Wilson relation and thus to the overlap operator. We study one-loop fermion contributions to the self-energy of the gauge field, which are related to the fermion contributions to the one-loop $\beta$ function and to the Weyl anomaly. We first explicitly demonstrate that the Ward identity is satisfied by the self-energy tensor. By performing careful analyses, we then obtain the correct self-energy tensor free of infra-red divergences, as a general consideration of the Weyl anomaly indicates. This demonstrates that our general operators give correct chiral and Weyl anomalies. In general, however, the Wilsonian effective action, which is supposed to be free of infra-red complications, is expected to be essential in the analyses of our general class of Dirac operators for dynamical gauge field.Comment: 30 pages. Some of the misprints were corrected. Phys. Rev. D (in press

Chiral properties of domain-wall fermions from eigenvalues of 4 dimensional Wilson-Dirac operator

We investigate chiral properties of the domain-wall fermion (DWF) system by using the four-dimensional hermitian Wilson-Dirac operator. We first derive a formula which connects a chiral symmetry breaking term in the five dimensional DWF Ward-Takahashi identity with the four dimensional Wilson-Dirac operator, and simplify the formula in terms of only the eigenvalues of the operator, using an ansatz for the form of the eigenvectors. For a given distribution of the eigenvalues, we then discuss the behavior of the chiral symmetry breaking term as a function of the fifth dimensional length. We finally argue the chiral property of the DWF formulation in the limit of the infinite fifth dimensional length, in connection with spectra of the hermitian Wilson-Dirac operator in the infinite volume limit as well as in the finite volume.Comment: Added a reference and modified the acknowledgmen

Non-perturbative renormalisation of left-left four-fermion operators with Neuberger fermions

We outline a general strategy for the non-perturbative renormalisation of composite operators in discretisations based on Neuberger fermions, via a matching to results obtained with Wilson-type fermions. As an application, we consider the renormalisation of the four-quark operators entering the Delta S=1 and Delta S=2 effective Hamiltonians. Our results are an essential ingredient for the determination of the low-energy constants governing non-leptonic kaon decays.Comment: 14 pages, 3 figure

Pythagoras' Theorem on a 2D-Lattice from a "Natural" Dirac Operator and Connes' Distance Formula

One of the key ingredients of A. Connes' noncommutative geometry is a generalized Dirac operator which induces a metric(Connes' distance) on the state space. We generalize such a Dirac operator devised by A. Dimakis et al, whose Connes' distance recovers the linear distance on a 1D lattice, into 2D lattice. This Dirac operator being "naturally" defined has the so-called "local eigenvalue property" and induces Euclidean distance on this 2D lattice. This kind of Dirac operator can be generalized into any higher dimensional lattices.Comment: Latex 11pages, no figure

The finite temperature QCD phase transition with domain wall fermions

The domain wall formulation of lattice fermions is expected to support accurate chiral symmetry, even at finite lattice spacing. Here we attempt to use this new fermion formulation to simulate two-flavor, finite temperature QCD near the chiral phase transition. In this initial study, a variety of quark masses, domain wall heights and domain wall separations are explored using an 8^3 x 4 lattice. Both the expectation value of the Wilson line and the chiral condensate show the temperature dependence expected for the QCD phase transition. Further, the desired chiral properties are seen for the chiral condensate, suggesting that the domain wall fermion formulation may be an effective approach for the numerical study of QCD at finite temperature.Comment: 44 pages, 15 figure

Dynamics of ripple formation on silicon surfaces by ultrashort laser pulses in sub-ablation conditions

An investigation of ultrashort pulsed laser induced surface modification due to conditions that result in a superheated melted liquid layer and material evaporation are considered. To describe the surface modification occurring after cooling and resolidification of the melted layer and understand the underlying physical fundamental mechanisms, a unified model is presented to account for crater and subwavelength ripple formation based on a synergy of electron excitation and capillary waves solidification. The proposed theoretical framework aims to address the laser-material interaction in sub-ablation conditions and thus minimal mass removal in combination with a hydrodynamics-based scenario of the crater creation and ripple formation following surface irradiation with single and multiple pulses, respectively. The development of the periodic structures is attributed to the interference of the incident wave with a surface plasmon wave. Details of the surface morphology attained are elaborated as a function of the imposed conditions and results are tested against experimental data