Lattice Chiral Gauge Theories in a Renormalizable Gauge

The lattice formulation of gauge theories in a renormalizable gauge is discussed. The formulation invokes a new phase diagram, and it may allow for a lattice definition of Chiral Gauge Theories.Comment: LaTeX, uses espcrc2.sty, 4 page

Renormalization-group blocking the fourth root of the staggered determinant

Lattice QCD simulations with staggered fermions rely on the ``fourth-root trick.'' The validity of this trick has been proved for free staggered fermions using renormalization-group block transformations. I review the elements of the construction and discuss how it might be generalized to the interacting case.Comment: Talk presented at Lattice 2005 (Improvement and Renormalization), Dublin, Ireland, and at the Workshop on Computational Hadron Physics, Nicosia, Cypru

Running coupling from gluon exchange in the Schrodinger functional

I propose a new method to determine the running coupling in a Schrodinger-functional setup. The method utilizes the scattering amplitude of massless fermions propagating between the time boundaries. Preliminary tests show the statistical fluctuations of the new observable to be about half those of the standard Schrodinger-functional running coupling.Comment: 5 pages, contribution to Lattice 201

Quantum Gravity via Random Triangulations of R^4 and Gravitons as Goldstone Bosons of SL(4)/O(4)

A model of random triangulations of a domain in $R^{(4)}$ is presented. The global symmetries of the model include SL(4) transformations and translations. If a stable microscopic scale exists for some range of parameters, the model should be in a translation invariant phase where SL(4) is spontaneously broken to O(4). In that phase, SL(4) Ward identities imply that the correlation length in the spin two channel of a symmetric tensor field is infinite. Consequently, it may be possible to identify the continuum limit of four dimensional Quantum Gravity with points inside that phase.Comment: WIS-94/44-PH, LaTeX, 20

Locality of the fourth root of the Staggered-fermion determinant: renormalization-group approach

Consistency of present-day lattice QCD simulations with dynamical (``sea'') staggered fermions requires that the determinant of the staggered-fermion Dirac operator, $det(D)$, be equal to $det^4(D_{rg}) det(T)$ where $D_{rg}$ is a local one-flavor lattice Dirac operator, and $T$ is a local operator containing only excitations with masses of the order of the cutoff. Using renormalization-group (RG) block transformations I show that, in the limit of infinitely many RG steps, the required decomposition exists for the free staggered operator in the ``flavor representation.'' The resulting one-flavor Dirac operator $D_{rg}$ satisfies the Ginsparg-Wilson relation in the massless case. I discuss the generalization of this result to the interacting theory.Comment: latex, 13 page

Better Domain-Wall Fermions

We discuss two modifications of domain-wall fermions, aimed to reduce the chiral-symmetry violations presently encountered in numerical simulations.Comment: 13 pages, contribution to workshop "Lattice Fermions and Structure of the Vacuum" (Dubna, Russia), uses crckapb.st

The large-mass regime of confining but nearly conformal gauge theories

We apply a recently developed dilaton-pion effective field theory for asymptotically free gauge theories near the conformal window to the $SU(3)$ gauge theory with $N_f=8$ fermions in the fundamental representation. Numerical data for this theory suggest the existence of a large-mass regime, where the fermion mass is not small but nevertheless the effective theory is applicable because of the parametric proximity of the conformal window. In this regime, we find that the mass dependence of hadronic quantities is similar to that of a a mass-deformed conformal theory, so that distinguishing infrared conformality from confinement requires the study of subleading effects.Comment: 6 pages, contribution to Lattice 201

Vacuum alignment and lattice artifacts: staggered fermions

In confining lattice gauge theories in which part of the flavor group is coupled weakly to additional gauge fields, both the dynamics of the weak gauge fields as well as lattice artifacts may have non-trivial effects on the orientation of the vacuum in flavor space. Here we discuss this issue for lattice gauge theories employing staggered fermions. Staggered fermions break flavor symmetries to a much smaller group on the lattice, and orientations in flavor space that are equivalent in the continuum may be distinct on the lattice. Assuming universality, we show that in the continuum limit the weakly gauged flavor symmetries are always vector-like, disproving a recent claim in the literature.Comment: Revtex, 19 pages. This replacement corrects a few minor errors in the published versio

Phase with no mass gap in non-perturbatively gauge-fixed Yang--Mills theory

An equivariantly gauge-fixed non-abelian gauge theory is a theory in which a coset of the gauge group, not containing the maximal abelian subgroup, is gauge fixed. Such theories are non-perturbatively well-defined. In a finite volume, the equivariant BRST symmetry guarantees that expectation values of gauge-invariant operators are equal to their values in the unfixed theory. However, turning on a small breaking of this symmetry, and turning it off after the thermodynamic limit has been taken, can in principle reveal new phases. In this paper we use a combination of strong-coupling and mean-field techniques to study an SU(2) Yang--Mills theory equivariantly gauge fixed to a U(1) subgroup. We find evidence for the existence of a new phase in which two of the gluons becomes massive while the third one stays massless, resembling the broken phase of an SU(2) theory with an adjoint Higgs field. The difference is that here this phase occurs in an asymptotically-free theory.Comment: Significant addition, conclusions unchanged. Revtex, 33 page

Dimensional transmutation in the longitudinal sector of equivariantly gauge-fixed Yang-Mills theory

We study the pure-gauge sector of an $SU(N)$ gauge theory, equivariantly gauge fixed to $SU(N-1)\times U(1)$, which is an asymptotically free non-linear sigma model in four dimensions. We show that dimensional transmutation takes place in the large-$N$ limit, and elaborate on the relevance of this result for a speculative scenario in which the strong longitudinal dynamics gives rise to a novel Higgs-Coulomb phase.Comment: 28 page