arXiv subjects

Yoshio Kikukawa

Publications and source records attributed to Yoshio Kikukawa.

At least 37 records · Page 2Linked to original sources

arXiv2007

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 Stückelberg 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.

hep-lat↗

arXiv2005

Electromagnetic mass difference on the lattice

We calculate electromagnetic mass difference of mesons using a method proposed by Duncan {\it et al}. The RG-improved gauge action and the non-compact Abelian gauge action are employed to generate configurations. Quark propagators in the range of $m_{PS}/m_{V}=0.76-0.51$ are obtained with the meanfield-improved clover quark action. Chiral and continuum extrapolations are performed and the results are compared with experiments. Finite size effects are also examined. Quark masses are extracted from the measured spectrum. Our preliminary values for light quark masses are $m_{u}^{\bar{MS}}(μ=2 {GeV}) = 3.03(19)$ MeV, $m_{d}^{\bar{MS}}(μ= 2 {GeV}) = 4.44(28)$ MeV, $m_{s}^{\bar{MS}}(μ= 2 {GeV}) = 99.2(52)$ MeV.

hep-lat↗

arXiv2005

Another approach to local cohomology problem in abelian lattice gauge theories

A new technique is proposed to classify a topological field in abelian lattice gauge theories. We perform the classification by regarding the topological field as a local composite field of the gauge field tensor instead of the vector potential associated to an admissible gauge field. Our method reproduces the result obtained by the ordinary method in the infinite four-dimensional lattice and can be extended to arbitrary higher dimensions. It also works in the direct cohomological analysis on a finite lattice.

hep-lat↗

arXiv2005

A local formulation of lattice Wess-Zumino model with exact $\U(1)_R$ symmetry

A lattice Wess-Zumino model is formulated on the basis of Ginsparg-Wilson fermions. In perturbation theory, our formulation is equivalent to the formulation by Fujikawa and Ishibashi and by Fujikawa. Our formulation is, however, free from a singular nature of the latter formulation due to an additional auxiliary chiral supermultiplet on a lattice. The model posssesses an exact $\U(1)_R$ symmetry as a supersymmetric counterpart of the Lüscher lattice chiral $\U(1)$ symmetry. A restration of the supersymmetric Ward-Takahashi identity in the continuum limit is analyzed in renormalized perturbation theory. In the one-loop level, a supersymmetric continuum limit is ensured by suitably adjusting a coefficient of a single local term $\tilde F^*\tilde F$. The non-renormalization theorem holds to this order of perturbation theory. In higher orders, on the other hand, coefficents of local terms with dimension $\leq4$ that are consistent with the $\U(1)_R$ symmetry have to be adjusted for a supersymmetric continuum limit. The origin of this complexicity in higher-order loops is clarified on the basis of the Reisz power counting theorem. Therefore, from a view point of supersymmetry, the present formulation is not quite better than a lattice Wess-Zumino model formulated by using Wilson fermions, although a number of coefficients which require adjustment is much less due to the exact $\U(1)_R$ symmetry. We also comment on an exact non-linear fermionic symmetry which corresponds to the one studied by Bonini and Feo; an existence of this exact symmetry itself does not imply a restoration of supersymmetry in the continuum limit without any adjustment of parameters.

hep-lat↗

arXiv2004

A numerical solution to the local cohomology problem in U(1) chiral gauge theories

We consider a numerical method to solve the local cohomology problem related to the gauge anomaly cancellation in U(1) chiral gauge theories. In the cohomological analysis of the chiral anomaly, it is required to carry out the differentiation and the integration of the anomaly with respect to the continuous parameter for the interpolation of the admissible gauge fields. In our numerical approach, the differentiation is evaluated explicitly through the rational approximation of the overlap Dirac operator with Zolotarev optimization. The integration is performed with a Gaussian Quadrature formula, which turns out to show rather good convergence. The Poincare lemma is reformulated for the finite lattice and is implemented numerically. We compute the current associated with the cohomologically trivial part of the chiral anomaly in two-dimensions and check its locality properties.

hep-lat↗

arXiv2003

Axial anomaly in the reduced model: Higher representations

The topological charge in the $\U(N)$ vector-like reduced model can be defined by using the overlap Dirac operator. We obtain its large $N$ limit for a fermion in a general gauge-group representation under a certain restriction of gauge field configurations which is termed $\U(1)$ embedding.

hep-lat↗

arXiv2003

Axial anomaly in the reduced model: Higher representations

The axial anomaly arising from the fermion sector of $\U(N)$ or $\SU(N)$ reduced model is studied under a certain restriction of gauge field configurations (the ``$\U(1)$ embedding'' with $N=L^d$). We use the overlap-Dirac operator and consider how the anomaly changes as a function of a gauge-group representation of the fermion. A simple argument shows that the anomaly vanishes for an irreducible representation expressed by a Young tableau whose number of boxes is a multiple of $L^2$ (such as the adjoint representation) and for a tensor-product of them. We also evaluate the anomaly for general gauge-group representations in the large $N$ limit. The large $N$ limit exhibits expected algebraic properties as the axial anomaly. Nevertheless, when the gauge group is $\SU(N)$, it does not have a structure such as the trace of a product of traceless gauge-group generators which is expected from the corresponding gauge field theory.

hep-lat↗

arXiv2002

Chiral anomalies in the reduced model

On the basis of an observation due to Kiskis, Narayanan and Neuberger, we show that there is a remnant of chiral anomalies in the reduced model when a Dirac operator which obeys the Ginsparg-Wilson relation is employed for the fermion sector. We consider fermions belonging to the fundamental representation of the gauge group U(N) or SU(N). For vector-like theories, we determine a general form of the axial anomaly or the topological charge within a framework of a U(1) embedding. For chiral gauge theories with the gauge group U(N), a remnant of gauge anomaly emerges as an obstruction to a smooth fermion integration measure. The pure gauge action of gauge-field configurations which cause these non-trivial phenomena always diverges in the 't Hooft $N\to\infty$ limit when d>2.

hep-lat↗

arXiv2002

Nicolai mapping vs. exact chiral symmetry on the lattice

Two-dimensional N=2 Wess-Zumino model is constructed on the lattice through Nicolai mapping with Ginsparg-Wilson fermion. The Nicolai mapping requires a certain would-be surface term in the bosonic action which ensures the vacuum energy cancellation even on the lattice, but inevitably breaks chiral symmetry. With the Ginsparg-Wilson fermion, the holomorphic structure of the would-be surface term is maintained, leaving a discrete subgroup of the exact chiral symmetry intact for a monomial scalar potential. By this feature both boson and fermion can be kept massless on the lattice without any fine-tuning.

hep-lat↗

arXiv2001

Analytic progress on exact lattice chiral symmetry

Theoretical issues of exact chiral symmetry on the lattice are discussed and related recent works are reviewed. For chiral theories, the construction with exact gauge invariance is reconsidered from the point of view of domain wall fermion. The issue in the construction of electroweak theory is also discussed. For vector-like theories, we discuss unitarity (positivity), Hamiltonian approach, and several generalizations of the Ginsparg-Wilson relation (algebraic and odd-dimensional).

hep-lat↗

arXiv2001

On the lattice construction of electroweak gauge theory

Based on the Ginsparg-Wilson relation, a gauge invariant formulation of electroweak SU(2)xU(1) gauge theory on the lattice is considered. If the hypercharge gauge coupling is turned off in the vacuum sector of the U(1) gauge fields, the theory consists of four left-handed SU(2) doublets and it is possible, as in vector-like theories, to make the fermion measure defined globally in all topological sectors of SU(2). We then try to incorporate U(1) gauge field, following Lüscher's reconstruction theorem. The global integrability condition is proved for ``gauge loops'' in the space of the U(1) gauge fields with arbitrary SU(2) gauge field fixed in the background. For ``non-gauge loops'', however, the proof is given so far only for the classical SU(2) instanton backgrounds.

hep-lat↗

arXiv2001

Domain wall fermion and chiral gauge theories on the lattice with exact gauge invariance

We discuss how to construct anomaly-free chiral gauge theories on the lattice with exact gauge invariance in the framework of domain wall fermion. Chiral gauge coupling is realized by introducing a five-dimensional gauge field which interpolates between two different four-dimensional gauge fields at boundaries. The five-dimensional dependence is compensated by a local and gauge-invariant counter term. The cohomology problem to obtain the counter term is formulated in 5+1 dimensional space, using the Chern-Simons current induced from the five-dimensional Wilson fermion. We clarify the connection to the invariant construction based on the Ginsparg-Wilson relation using overlap Dirac operator. Formula for the measure and the effective action of Weyl fermions are obtained in terms of five-dimensional lattice quantities.

hep-lat↗

arXiv2000

Gauge anomaly cancellations in SU(2)_L \times U(1)_Y Electroweak theory on the lattice

We consider the cohomological classification of the 4+2-dimensional topological field, which is proposed by Lüscher, for SU(2)_L \times U(1)_Y electroweak theory. The dependence on the admissible abelian gauge field of U(1)_Y is determined through topological argument, with SU(2)_L gauge field fixed as background. We then show the exact cancellation of the local gauge anomaly of the mixed type {SU(2)_L}^2 \times U(1)_Y at finite lattice spacing, as well as {U(1)_Y}^3, using the pseudo reality of SU(2)_L and the anomaly cancellation conditions in the electroweak theory given in terms of the hyper-charges of U(1)_Y.

hep-lat↗

arXiv2000

A lattice implementation of the eta-invariant and effective action for chiral fermions on the lattice

We consider a lattice implementation of the eta-invariant, using the complex phase of the determinant of the simplified domain-wall fermion, which couples to an interpolating five-dimensional gauge field. We clarify the relation to the effective action for chiral Ginsparg-Wilson fermions. The integrability, which holds true for anomaly-free theories in the classical continuum limit, is not assured on the lattice with a finite spacing. A lattice expression for the five-dimensional Chern-Simons term is obtained.

hep-lat↗

arXiv2000

Locality bound for effective four-dimensional action of domain-wall fermion

We discuss locality in the domain-wall QCD through the effective four-dimensional Dirac operator which is defined by the transfer matrix of the five-dimensional Wilson fermion. We first derive an integral representation for the effective operator, using the inverse five-dimensional Wilson-Dirac operator with the anti-periodic boundary condition in the fifth direction. Exponential bounds are obtained from it for gauge fields with small lattice field strength.

hep-lat↗

arXiv1999

Low energy effective action of domain-wall fermion and the Ginsparg-Wilson relation

We derive the effective action of the light fermion field of the domain-wall fermion, which is referred as q(x) and \bar q(x) by Furman and Shamir. The inverse of the effective Dirac operator turns out to be identical to the inverse of the truncated overlap Dirac operator except a local contact term, which would give the chiral symmetry breaking in the Ginsparg-Wilson relation. We argue that there are direct relations between the low energy observables of the domain-wall QCD and observables of the Ginsparg-Wilson fermion described by the (truncated) overlap Dirac operator.

hep-lat↗

arXiv1998

A note on the exact lattice chiral symmetry in the overlap formalism

Using the grassman-number-integral representation of the vacuum overlap formula, it is shown that the symmetry of the auxiliary quantum fermion system in the overlap formalism induces exact chiral symmetry of the action of the type given by Luscher under the chiral transformation $δψ_n = γ_5(1-a D)ψ_n$ and $ δ\bar ψ_n = \bar ψ_n γ_5$. With this relation, we consider the connection between the covariant form of the anomaly discussed in the context of the overlap formula and the axial anomaly associated to the exact chiral symmetry in the action formalism. The covariant gauge current in the overlap formalism is translated to the action formalism and its explicit expression is obtained.

hep-lat↗

arXiv1998

Axial vector current of exact chiral symmetry on the lattice

We discuss the exact chiral symmetry and its spontaneous breakdown in lattice QCD with the Dirac operators satisfying the Ginsparg-Wilson relation. The axial vector current, which turns out to be related to the vector current simply by the insertion of the operator γ_5 (1-aD), is explicitly constructed in the case of the Neuberger-Dirac operator. We also consider an Euclidean proof of the Nambu-Goldstone theorem using the Ward-Takahashi identity of this symmetry.

hep-lat↗