Searcharxiv⌕ Search

arXiv subjects

Yigal Shamir

Publications and source records attributed to Yigal Shamir.

At least 109 records · Page 6Linked to original sources
arXiv2000

Overlap-Dirac fermions with a small hopping parameter

We consider overlap-Dirac fermions at non-zero bare coupling and for a small hopping parameter, or, equivalently, large $|M|$ with $M$ the domain-wall height. We prove the existence of a phase at large positive $M$ where the abelian axial group $U_A(1)$ is a symmetry, and the corresponding pseudo-scalar is an exact Goldstone boson. We also provide a conjecture for the phase diagram of asymptotically free gauge theories with overlap-Dirac fermions. In particular, we suggest that, for large gauge coupling, the massive-fermion phase at negative $M$ possibly extends to all $M<4$.

hep-lat↗
arXiv2000

New Domain-Wall Fermion Actions

In perturbation theory, the wave function of domain-wall quarks decreases exponentially with the fifth coordinate. We show that, regardless of the quark's own momentum, the fall-off rate of the one-loop wave function is equal to the slowest rate encountered at tree-level for any lattice four-momentum. We propose new domain-wall actions involving beyond-nearest neighbor couplings in the four physical dimensions, for which the perturbative wave function decreases much faster. It is hoped that the new actions may preserve the good chiral properties of domain-wall fermions up to larger values of the lattice spacing.

hep-lat↗
arXiv1999

Better Domain-Wall Fermions

We discuss two modifications of domain-wall fermions, aimed to reduce the chiral-symmetry violations presently encountered in numerical simulations.

hep-lat↗
arXiv1999

Abelian and Nonabelian Lattice Chiral Gauge Theories through Gauge Fixing

After an introduction in which we review the fundamental difficulty in constructing lattice chiral gauge theories, we summarize the analytic and numerical evidence that abelian lattice chiral gauge theories can be nonperturbatively constructed through the gauge-fixing approach. In addition, we indicate how we believe that the method may be extended to nonabelian chiral gauge theories.

hep-lat↗
arXiv1999

The Phase Diagram and Spectrum of Gauge-Fixed Abelian Lattice Gauge Theory

We consider a lattice discretization of a covariantly gauge-fixed abelian gauge theory. The gauge fixing is part of the action defining the theory, and we study the phase diagram in detail. As there is no BRST symmetry on the lattice, counterterms are needed, and we construct those explicitly. We show that the proper adjustment of these counterterms drives the theory to a new type of phase transition, at which we recover a continuum theory of (free) photons. We present both numerical and (one-loop) perturbative results, and show that they are in good agreement near this phase transition. Since perturbation theory plays an important role, it is important to choose a discretization of the gauge-fixing action such that lattice perturbation theory is valid. Indeed, we find numerical evidence that lattice actions not satisfying this requirement do not lead to the desired continuum limit. While we do not consider fermions here, we argue that our results, in combination with previous work, provide very strong evidence that this new phase transition can be used to define abelian lattice chiral gauge theories.

hep-lat↗
arXiv1999

New tests of the gauge-fixing approach to lattice chiral gauge theories

We report on recent progress with the gauge-fixing approach to lattice chiral gauge theories. The bosonic sector of the gauge-fixing approach is studied with fully dynamical U(1) gauge fields. We demonstrate that it is important to formulate the Lorentz gauge-fixing action such that the dense set of lattice Gribov copies is removed, and the gauge-fixing action has a unique absolute minimum. We then show that the spectrum in the continuum limit contains only the desired massless photon, as expected.

hep-lat↗
arXiv1998

Reducing Chiral Symmetry Violations in Lattice QCD with Domain-Wall Fermions

The inverse of the fermion matrix squared is used to define a transfer matrix for domain-wall fermions. When the domain-wall height $M$ is bigger than one, the transfer matrix is complex. Slowly suppressed chiral symmetry violations may then arise from all eigenvalues of the transfer matrix which are located near the unit circle. Using a variable lattice spacing for the fifth coordinate we enforce the strict positivity of the transfer matrix for any $M$. We furthermore propose a modified pseudo-fermion action, aimed to decrease the density of close-to-unity eigenvalues of the (positive) transfer matrix, at the price of a small renormalization of the coupling constant. We explain why these changes may reduce chiral symmetry violations in lattice QCD simulations.

hep-lat↗
arXiv1998

More on Lattice BRST Invariance

In the gauge-fixing approach to (chiral) lattice gauge theories, the action in the U(1) case implicitly contains a free ghost term, in accordance with the continuum abelian theory. On the lattice there is no BRST symmetry and, without fermions, the partition function is strictly positive. Recently, Neuberger pointed out in hep-lat/9801029 that a different choice of the ghost term would lead to a BRST-invariant lattice model, which is ill-defined nonperturbatively. We show that such a lattice model is inconsistent already in perturbation theory, and clearly different from the gauge-fixing approach.

hep-lat↗
arXiv1998

Gauge-fixing approach to lattice chiral gauge theories

We review the status of our recent work on the gauge-fixing approach to lattice chiral gauge theories. New numerical results in the reduced version of a model with a U(1) gauge symmetry are presented which strongly indicate that the factorization of the correlation functions of the left-handed neutral and right-handed charged fermion fields, which we established before in perturbation theory, holds also nonperturbatively.

hep-lat↗
arXiv1998

Lattice Chiral Fermions Through Gauge Fixing

We study a concrete lattice regularization of a U(1) chiral gauge theory. We use Wilson fermions, and include a Lorentz gauge-fixing term and a gauge-boson mass counterterm. For a reduced version of the model, in which the gauge fields are constrained to the trivial orbit, we show that there are no species doublers, and that the fermion spectrum contains only the desired states in the continuum limit, namely charged left-handed (LH) fermions and neutral right-handed (RH) fermions.

hep-lat↗
arXiv1998

Chiral Fermions on the Lattice through Gauge Fixing -- Perturbation Theory

We study the gauge-fixing approach to the construction of lattice chiral gauge theories in one-loop weak-coupling perturbation theory. We show how infrared properties of the gauge degrees of freedom determine the nature of the continuous phase transition at which we take the continuum limit. The fermion self-energy and the vacuum polarization are calculated, and confirm that, in the abelian case, this approach can be used to put chiral gauge theories on the lattice in four dimensions. We comment on the generalization to the nonabelian case.

hep-lat↗
arXiv1997

The Standard Model from a New Phase Transition on the Lattice

Several years ago it was conjectured in the so-called Roma Approach, that gauge fixing is an essential ingredient in the lattice formulation of chiral gauge theories. In this paper we discuss in detail how the gauge-fixing approach may be realized. As in the usual (gauge invariant) lattice formulation, the continuum limit corresponds to a gaussian fixed point, that now controls both the transversal and the longitudinal modes of the gauge field. A key role is played by a new phase transition separating a conventional Higgs or Higgs-confinement phase, from a phase with broken rotational invariance. In the continuum limit we expect to find a scaling region, where the lattice correlators reproduce the euclidean correlation functions of the target (chiral) gauge theory, in the corresponding continuum gauge.

hep-lat↗
arXiv1997

On the Phase Diagram of a Lattice U(1) Gauge Theory with Gauge Fixing

As a first step towards a nonperturbative investigation of the gauge-fixing (Rome) approach to lattice chiral gauge theories we study a U(1) model with an action that includes a local gauge-fixing term and a mass counterterm for the gauge fields. The model is studied on the trivial orbit so that only the dynamics of the longitudinal gauge degrees of freedom is taken into account. The phase diagram of this higher-derivative scalar field theory is determined, both in the mean-field approximation and numerically. The continuum limit of the model corresponds to a continuous phase transition between a ferromagnetic (FM) phase where the global U(1) symmetry is broken, and a so-called helicoidal ferromagnetic (FMD) phase with broken U(1) symmetry and a nonvanishing condensate of the vector field. The global U(1) symmetry is restored in this continuum limit. We show that our data for the magnetization in the FM and FMD phases are in good agreement with perturbation theory.

hep-lat↗
arXiv1996

A Gauge-Fixing Action for Lattice Gauge Theories

We present a lattice gauge-fixing action $S_{gf}$ with the following properties: (a) $S_{gf}$ is proportional to the trace of $(\sum_μ\partial_μA_μ)^2$, plus irrelevant terms of dimension six and higher; (b) $S_{gf}$ has a unique absolute minimum at $U_{x,μ}=I$. Noting that the gauge-fixed action is not BRST invariant on the lattice, we discuss some important aspects of the phase diagram.

hep-lat↗
arXiv1996

A Supersymmetry Anomaly

A supersymmetry anomaly is found in the presence of non-perturbative fields. When the action is expressed in terms of the correct quantum variables, anomalous surface terms appear in its supersymmetric variation - one per each collective coordinate. The anomalous surface terms do not vanish in general when inserted in two- or higher-loop bubble diagrams, and generate a violation of the SUSY Ward identities.

hep-th↗
arXiv1995

The relation between the waveguide and overlap implementations of Kaplan's domain wall fermions

Recently, Narayanan and Neuberger proposed that the fermion determinant for a lattice chiral gauge theory be defined by an overlap formula. The motivation for that formula comes from Kaplan's five dimensional lattice domain wall fermions. In the case that the target continuum theory contains $4n$ chiral families, we show that the effective action defined by overlap formula is identical to the effective action of a modified waveguide model that has extra bosonic ghost fields. This raises serious questions about the viability of the overlap formula for defining chiral gauge theories on the lattice.

hep-lat↗
arXiv1995

Lattice Chiral Fermions

I review the ongoing attempts to define chiral gauge theories using the lattice regularization.

hep-lat↗