Nontriviality of Gauge-Higgs-Yukawa System and Renormalizability of Gauged NJL Model

In the leading order of a modified 1/Nc expansion, we show that a class of gauge-Higgs-Yukawa systems in four dimensions give non-trivial and well-defined theories in the continuum limit. The renormalized Yukawa coupling y and the quartic scalar coupling \lambda have to lie on a certain line in the (y,\lambda) plane and the line terminates at an upper bound. The gauged Nambu--Jona-Lasinio (NJL) model in the limit of its ultraviolet cutoff going to infinity, is shown to become equivalent to the gauge-Higgs-Yukawa system with the coupling constants just on that terminating point. This proves the renormalizability of the gauged NJL model in four dimensions. The effective potential for the gauged NJL model is calculated by using renormalization group technique and confirmed to be consistent with the previous result by Kondo, Tanabashi and Yamawaki obtained by the ladder Schwinger-Dyson equation.Comment: 32 pages, LaTeX, 3 Postscript Figures are included as uuencoded files (need `epsf.tex'), KUNS-1278, HE(TH) 94/10 / NIIG-DP-94-2. (Several corrections in the introduction and references.

Four-dimensional lattice chiral gauge theories with anomalous fermion content

In continuum field theory, it has been discussed that chiral gauge theories with Weyl fermions in anomalous gauge representations (anomalous gauge theories) can consistently be quantized, provided that some of gauge bosons are permitted to acquire mass. Such theories in four dimensions are inevitablly non-renormalizable and must be regarded as a low-energy effective theory with a finite ultraviolet (UV) cutoff. In this paper, we present a lattice framework which enables one to study such theories in a non-perturbative level. By introducing bare mass terms of gauge bosons that impose ``smoothness'' on the link field, we explicitly construct a consistent fermion integration measure in a lattice formulation based on the Ginsparg-Wilson (GW) relation. This framework may be used to determine in a non-perturbative level an upper bound on the UV cutoff in low-energy effective theories with anomalous fermion content. By further introducing the St\"uckelberg or Wess-Zumino (WZ) scalar field, this framework provides also a lattice definition of a non-linear sigma model with the Wess-Zumino-Witten (WZW) term.Comment: 18 pages, the final version to appear in JHE

Solving the local cohomology problem in U(1) chiral gauge theories within a finite lattice

In the gauge-invariant construction of abelian chiral gauge theories on the lattice based on the Ginsparg-Wilson relation, the gauge anomaly is topological and its cohomologically trivial part plays the role of the local counter term. We give a prescription to solve the local cohomology problem within a finite lattice by reformulating the Poincar\'e lemma so that it holds true on the finite lattice up to exponentially small corrections. We then argue that the path-integral measure of Weyl fermions can be constructed directly from the quantities defined on the finite lattice.Comment: revised version, 35pages, using JHEP3.cl

A simple construction of fermion measure term in U(1) chiral lattice gauge theories with exact gauge invariance

In the gauge invariant formulation of U(1) chiral lattice gauge theories based on the Ginsparg-Wilson relation, the gauge field dependence of the fermion measure is determined through the so-called measure term. We derive a closed formula of the measure term on the finite volume lattice. The Wilson line degrees of freedom (torons) of the link field are treated separately to take care of the global integrability. The local counter term is explicitly constructed with the local current associated with the cohomologically trivial part of the gauge anomaly in a finite volume. The resulted formula is very close to the known expression of the measure term in the infinite volume with a single parameter integration, and would be useful in practical implementations.Comment: 25 pages, uses JHEP3.cls, the version to appear in JHE

A construction of the Glashow-Weinberg-Salam model on the lattice with exact gauge invariance

We present a gauge-invariant and non-perturbative construction of the Glashow-Weinberg-Salam model on the lattice, based on the lattice Dirac operator satisfying the Ginsparg-Wilson relation. Our construction covers all SU(2) topological sectors with vanishing U(1) magnetic flux and would be usable for a description of the baryon number non-conservation. In infinite volume, it provides a gauge-invariant regularization of the electroweak theory to all orders of perturbation theory. First we formulate the reconstruction theorem which asserts that if there exists a set of local currents satisfying cetain properties, it is possible to reconstruct the fermion measure which depends smoothly on the gauge fields and fulfills the fundamental requirements such as locality, gauge-invariance and lattice symmetries. Then we give a closed formula of the local currents required for the reconstruction theorem.Comment: 32 pages, uses JHEP3.cls, the version to appear in JHE

Domain wall fermions in vector gauge theories

I review domain wall fermions in vector gauge theories. Following a brief introduction, the status of lattice calculations using domain wall fermions is presented. I focus on results from QCD, including the light quark masses and spectrum, weak matrix elements, the $n_f=2$ finite temperature phase transition, and topology and zero modes and conclude with topics for future study.Comment: LATTICE98. Plenary review talk. LaTeX(espcrc2.sty), 13 pages, 17 eps figure

Lattice chiral fermions in the background of non-trivial topology

We address the problem of numerical simulations in the background non-trivial topology in the chiral Schwinger model. An effective fermionic action is derived which is in accord with established analytical results, and which satisfies the anomaly equation. We describe a numerical evaluation of baryon number violating amplitudes, specifically the 't Hooft vertex.Comment: LATTICE99(Chiral Gauge Theories