Non-perturbative BRST invariance and what it might be good for

We construct a local, gauge-fixed, lattice Yang-Mills theory with an exact BRST invariance, and with the same perturbative expansion as the standard Yang-Mills theory. The ghost sector, and some of its BRST transformation rules, are modified to get around Neuberger's theorem. A special term is introduced in the action to regularize the Gribov horizons, and the limit where the regulator is removed is discussed. We conclude with a few comments on what might be the physical significance of this theory. We speculate that there may exist new strong-interaction phases apart from the anticipated confinement phase.Comment: 3 pages, Lattice2002(theoretical), For additional technical details see ref.

Quenching effects in strong penguin contributions to ϵ′/ϵ\epsilon'/\epsilon

Quenching effects in strong penguin matrix elements are investigated. A lattice determination of $\alpha_q^{NS}$, the constant that appears in the quenched ChPT relevant for the lattice analysis of $K\to\pi\pi$ matrix elements, shows that this constant is large. The original RBC analysis of $Q_6$ matrix elements is revisited in light of this result. Also, the numerical effects of choosing the singlet Golterman-Pallante method of quenching $Q_6$ is investigated.Comment: 3 pages, talk presented at Lattice2004(weak), Fermilab, June 21-26, 200

On tadpole improvement for staggered fermions

An explanation is proposed for the fact that Lepage--Mackenzie tadpole improvement does not work well for staggered fermions. The idea appears to work for all renormalization constants which appear in the staggered fermion self-energy. Wilson fermions are also discussed.Comment: LATTICE98(improvement), 3 pages, 1 figure, latex, uses espcrc2.sty, epsf.st

Why the overlap formula does not lead to chiral fermions

We describe a conceptually simple, but important test for the overlap approach to the construction of lattice chiral gauge theories. We explain the equivalence of the overlap formula with a certain waveguide model for a simple set of gauge configurations (the trivial orbit). This equivalence is helpful in carrying out the test, and casts serious doubts on the viability of the overlap approach. A recent note by Narayanan and Neuberger which points out a mistake in our previous work is irrelevant in this context.Comment: 4 pages, compressed postscript, contribution to Lattice'9

Manifestly Gauge Invariant Models of Chiral Lattice Fermions

A manifestly gauge invariant lattice action for nonanomalous chiral models is proposed which leads in the continuum limit to the theory free of doublers.Comment: 9 pages, LaTeX. Revised version with an extended discussion of the role of higher derivative regulators. Submitted to Phys.Lett.B. Preprint SMI-9-9

SU(N) chiral gauge theories on the lattice: a quick overview

We describe how an SU(N) chiral gauge theory can be put on the lattice using non-perturbative gauge fixing. In particular, we explain how the Gribov problem is dealt with. Our construction is local, avoids doublers, and weak-coupling perturbation theory applies at the critical point which defines the continuum limit of our lattice chiral gauge theory.Comment: Parallel talk presented at Lattice2004(chiral), Fermilab, June 21-26, 200

Is there an Aoki phase in quenched QCD?

We argue that quenched QCD has non-trivial phase structure for negative quark mass, including the possibility of a parity-flavor breaking Aoki phase. This has implications for simulations with domain-wall or overlap fermions.Comment: Parallel talk presented at Lattice2004(spectrum), Fermilab, June 21-26, 200

Chiral Perturbation Theory, Non-leptonic Kaon Decays, and the Lattice

In this talk, I first motivate the use of Chiral Perturbation Theory in the context of Lattice QCD. In particular, I explain how partially quenched QCD, which has, in general, unequal valence- and sea-quark masses, can be used to obtain real-world (i.e. unquenched) results for low-energy constants. In the second part, I review how Chiral Perturbation Theory may be used to overcome theoretical difficulties which afflict the computation of non-leptonic kaon decay rates from Lattice QCD. I argue that it should be possible to determine at least the O(p^2) weak low-energy constants reliably from numerical computations of the K to pi and K to vacuum matrix elements of the corresponding weak operators.Comment: 13 pages, invited plenary talk at Chiral 2000, Jefferson Lab., July 17-22, 200