338 research outputs found
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 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
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