36 research outputs found
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
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
Towards Weyl fermions on the lattice without artefacts
In spite of the breakthrough in non-perturbative chiral gauge theories during
the last decade, the present formulation has stubborn artefacts. Independently
of the fermion representation one is confronted with unwanted CP violation and
infinitely many undetermined weight factors. Renormalization group identifies
the culprit. We demonstrate the procedure on Weyl fermions in a real
representation
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
Chiral Lattice Gauge Theories Via Mirror-Fermion Decoupling: A Mission (im)Possible?
This is a review of the status and outstanding issues in attempts to
construct chiral lattice gauge theories by decoupling the mirror fermions from
a vectorlike theory. In the first half, we explain why studying nonperturbative
chiral gauge dynamics may be of interest, enumerate the problems that a lattice
formulation of chiral gauge theories must overcome, and briefly review our
current knowledge. We then discuss the motivation and idea of mirror-fermion
decoupling and illustrate the desired features of the decoupling dynamics by a
simple solvable toy model. The role of exact chiral symmetries and matching of
't Hooft anomalies on the lattice is also explained. The second, more
technical, half of the article is devoted to a discussion of the known and
unknown features of mirror-decoupling dynamics formulated with Ginsparg-Wilson
fermions. We end by pointing out possible directions for future studies.Comment: 53 pp; 6 figs; added table of contents, references, fixed typo
Lattice formulation of two-dimensional N=(2,2) super Yang-Mills with SU(N) gauge group
We propose a lattice model for two-dimensional SU(N) N=(2,2) super Yang-Mills
model. We start from the CKKU model for this system, which is valid only for
U(N) gauge group. We give a reduction of U(1) part keeping a part of
supersymmetry. In order to suppress artifact vacua, we use an admissibility
condition.Comment: 16 pages, 3 figures; v2: typo crrected; v3: 18 pages, a version to
appear in JHE