arXiv subjects

Yigal Shamir

Publications and source records attributed to Yigal Shamir.

119 records · Page 7Linked to original sources

arXiv1995

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.

hep-lat↗

arXiv1994

Axial symmetries in lattice QCD with Kaplan fermions

This paper develops in detail a lattice definition of QCD based on the chiral defect fermions recently introduced by Kaplan. The revised version provides missing technical details in the proof that non-singlet axial symmetries become exact in the limit of an infinite fifth dimension. Also several minor errors are corrected.

hep-lat↗

arXiv1994

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.

hep-th↗

arXiv1994

Domain wall fermions in a waveguide: the phase diagram at large Yukawa coupling

In this paper we return to a model with domain wall fermions in a waveguide. This model contains a Yukawa coupling $y$ which is needed for gauge invariance. A previous paper left the analysis for large values of this coupling incomplete. We fill the gap by developing a systematic expansion suitable for large $y$, and using this, we gain an analytic understanding of the phase diagram and fermion spectrum. We find that in a sense all the species doublers come back for large $y$. The conclusion that no lattice chiral gauge theory can be obtained from this approach therefore remains valid.

hep-lat↗

arXiv1994

Dynamical-Space Regular-Time Lattice and Induced Gravity

It is proposed that gravity may arise in the low energy limit of a model of matter fields defined on a special kind of a dynamical random lattice. Time is discretized into regular intervals, whereas the discretization of space is random and dynamical. A triangulation is associated to each distribution of the spacetime points using the flat metric of the embedding space. We introduce a diffeomorphism invariant, bilinear scalar action, but no ``pure gravity'' action. Evidence for the existence of a non-trivial continuum limit is provided by showing that the zero momentum scalar excitation has a finite energy in the limit of vanishing lattice spacing. Assuming the existence of localized low energy states which are described by a natural set of observables, we show that an effective curved metric will be induced dynamically. The components of the metric tensor are identified with quasi-local averages of certain microscopic properties of the quantum spacetime. The Planck scale is identified with the highest mass scale of the matter sector.

hep-th↗

arXiv1993

Anomalies and chiral defect fermions

Chiral defect fermions in the background of an external, $2n$ dimensional gauge field are considered. Assuming first a finite extra dimension, we calculate the axial anomaly in a vector-like, gauge invariant model for arbitrary $n$, and the consistent anomaly in a gauge {\it variant} model with a chiral spectrum. For technical reasons, the latter calculation is limited to the $2+1$ dimensional case. We also show that the infinite lattice chiral model, when properly defined, is in fact a limiting case of the above gauge-variant model. The behaviour of this model with a dynamical gauge field is discussed.

hep-lat↗

arXiv1993

On the absence of chiral fermions in interacting lattice theories

We consider interacting theories with a compact internal symmetry group on a regular lattice. We show that the spectrum is necessarily vector-like provided the following conditions are satisfied: (a)~weak form of locality, (b)~relativistic continuum limit without massless bosons, and (c)~pole-free effective vertex functions for conserved currents. The proof exploits the zero frequency inverse retarded propagator of an appropriate set of interpolating fields as an effective quadratic hamiltonian, to which the Nielsen-Ninomiya theorem is applied. The main results of this paper have been reported in WIS-93/56-JUNE-PH, hep-lat/9306023.

hep-lat↗

arXiv1993

Constraints on the Existence of Chiral Fermions in Interacting Lattice Theories

It is shown that an interacting theory, defined on a regular lattice, must have a vector-like spectrum if the following conditions are satisfied: (a)~locality, (b)~relativistic continuum limit without massless bosons, and (c)~pole-free effective vertex functions for conserved currents. The proof exploits the zero frequency inverse retarded propagator of an appropriate set of interpolating fields as an effective quadratic hamiltonian, to which the Nielsen-Ninomiya theorem is applied.

hep-lat↗

arXiv1993

Chiral Fermions from Lattice Boundaries

We construct a model in which four dimensional chiral fermions arise on the boundaries of a five dimensional lattice with free boundary conditions in the fifth direction. The physical content is similar to Kaplan's model of domain wall fermions, yet the present construction has several technical advantages. We discuss some aspects of perturbation theory, as well as possible applications of the model both for lattice QCD and for the on-going attempts to construct a lattice chiral gauge theory.

hep-lat↗

arXiv1992

The Euclidean Spectrum of Kaplan's Lattice Chiral Fermions

We consider the (2n+1)-dimensional euclidean Dirac operator with a mass term that looks like a domain wall, recently proposed by Kaplan to describe chiral fermions in $2n$ dimensions. In the continuum case we show that the euclidean spectrum contains {\it no} bound states with non-zero momentum. On the lattice, a bound state spectrum without energy gap exists only if $m$ is fine tuned to some special values, and the dispersion relation does not describe a relativistic fermion. In spite of these peculiarities, the fermionic propagator {\it has} the expected (1/p-slash) pole on the domain wall. But there may be a problem with the phase of the fermionic determinant at the non-perturbative level.

hep-lat↗

arXiv1992

Compensating Fields and Anomalies in Supergravity

We discuss the quantization of theories which are formulated using compensating fields. In particular, we discuss the relation between the components formulation and the superspace formulation of supergravity theories. The requirement that the compensating field can be eliminated at the quantum level gives rise to on-shell constraints on the operators of the theory. In some cases, the constraints turn out to be physically unacceptable. Using these considerations we show that new minimal supergravity is in general anomalous.

hep-th↗