Ginsparg-Wilson Relation and Ultralocality

It is shown that it is impossible to construct a free theory of fermions on infinite hypercubic Euclidean lattice in four dimensions that is: (a) ultralocal, (b) respects symmetries of hypercubic lattice, (c) corresponding kernel satisfies D gamma5 + gamma5 D = D gamma5 D (Ginsparg-Wilson relation), (d) describes single species of massless Dirac fermions in the continuum limit.Comment: 4 pages, REVTEX; few minor change

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

Topological Charge Membranes in 2D and 4D Gauge Theory

Local topological charge structure in the 2D CP(N-1) sigma models is studied using the overlap Dirac operator. Long-range coherence of topological charge along locally 1D regions in 2D space-time is observed. We discuss the connection between these results and the recent discovery of coherent 3D sheets of topological charge in 4D QCD. In both cases, coherent regions of topological charge form along surfaces of approximmate codimension 1.Comment: Lattice2004(topology

Mixed Action Simulations on Staggered Background; Interpretation and Result for the 2-flavor QCD Chiral Condensate

Growing evidence indicates that in the continuum limit the rooted staggered action is in the correct QCD universality class, the non-local terms arising from taste breaking can be viewed as lattice artifacts. In this paper we consider the 2-flavor Asqtad staggered action at a lattice spacing of approximately 0.13 fm and probe the properties of the staggered configurations by an overlap valence Dirac operator. By comparing the distribution of the overlap eigenmodes to continuum QCD predictions we investigate if/when the lattice artifacts are small as a function of the staggered quark mass. We define a matching overlap quark mass where the lattice corrections are minimal for the topological susceptibility and from the eigenmode distribution we predict the 2-flavor chiral condensate. Our results indicate that the staggered configurations are consistent with 2-flavor continuum QCD up to small lattice artifacts, and predict a consistent value for the infinite volume chiral condensate.Comment: 12 pages, 6 figures, REVTeX

Ginsparg-Wilson relation and the overlap formula

The fermionic determinant of a lattice Dirac operator that obeys the Ginsparg-Wilson relation factorizes into two factors that are complex conjugate of each other. Each factor is naturally associated with a single chiral fermion and can be realized as a overlap of two many body vacua.Comment: 4 pages, plain tex, no figure

Solutions of the Ginsparg-Wilson Relation

We analyze general solutions of the Ginsparg-Wilson relation for lattice Dirac operators and formulate a necessary condition for such operators to have non-zero index in the topologically nontrivial background gauge fields.Comment: 6 pages, latex, no figures, set T to 1 in eqs. (10)--(13

Static quarks with improved statistical precision

We present a numerical study for different discretisations of the static action, concerning cut-off effects and the growth of statistical errors with Euclidean time. An error reduction by an order of magnitude can be obtained with respect to the Eichten-Hill action, for time separations beyond 1.3 fm, keeping discretization errors small. The best actions lead to a big improvement on the precision of the quark mass Mb and F_Bs in the static approximation.Comment: 3 pages, 4 figures, Lattice2003(heavy

Ginsparg-Wilson-Luscher Symmetry and Ultralocality

Important recent discoveries suggest that Ginsparg-Wilson-Luscher (GWL) symmetry has analogous dynamical consequences for the theory on the lattice as chiral symmetry does in the continuum. While it is well known that inherent property of lattice chiral symmetry is fermion doubling, we show here that inherent property of GWL symmetry is that the infinitesimal symmetry transformation couples fermionic degrees of freedom at arbitrarily large lattice distances (non-ultralocality). The consequences of this result for ultralocality of symmetric actions are discussed.Comment: 18 pages, LATEX. For clarity changed to infinitesimal transformations, typos corrected, explicit hypothesis adde

The Square-Lattice Heisenberg Antiferromagnet at Very Large Correlation Lengths

The correlation length of the square-lattice spin-1/2 Heisenberg antiferromagnet is studied in the low-temperature (asymptotic-scaling) regime. Our novel approach combines a very efficient loop cluster algorithm -- operating directly in the Euclidean time continuum -- with finite-size scaling. This enables us to probe correlation lengths up to $\xi \approx 350,000$ lattice spacings -- more than three orders of magnitude larger than any previous study. We resolve a conundrum concerning the applicability of asymptotic-scaling formulae to experimentally- and numerically-determined correlation lengths, and arrive at a very precise determination of the low-energy observables. Our results have direct implications for the zero-temperature behavior of spin-1/2 ladders.Comment: 12 pages, RevTeX, plus two Postscript figures. Some minor modifications for final submission to Physical Review Letters. (accepted by PRL

Global obstructions to gauge-invariance in chiral gauge theory on the lattice

It is shown that certain global obstructions to gauge-invariance in chiral gauge theory, described in the continuum by Alvarez-Gaume and Ginsparg, are exactly reproduced on the lattice in the Overlap formulation at small non-zero lattice spacing (i.e. close to the classical continuum limit). As a consequence, the continuum anomaly cancellation condition $d_R^{abc}=0$ is seen to be a necessary (although not necessarily sufficient) condition for anomaly cancellation on the lattice in the Overlap formulation.Comment: 31 pages, latex. v4: A few minor corrections, to appear in Nucl. Phys.