arXiv subjects

Yoshio Kikukawa

Publications and source records attributed to Yoshio Kikukawa.

44 records · Page 3Linked to original sources

arXiv1998

Overlap formula for the chiral multiplet

The vacuum overlap formalism is extended to describe the supersymmetric multiplet of a Weyl fermion, a complex scalar boson and an auxiliary field in the case without interaction, based on the fact that supersymmetry can be maintained upto quadratic terms by introducing bosonic species doublers. We also obtain a local action which describes the chiral multiplet and discuss its symmetry structure. It is shown that, besides the manifest supersymmetry, the action possesses a chiral symmetry of the type given by Lüscher and analogous bosonic symmetries which may be regarded as independent infinitesimal rotations of complex phases of the scalar and the auxiliary fields. This implies that the $U(1) \times U(1)_R$ symmetry of the chiral multiplet can be exact on the lattice.

hep-lat↗

arXiv1997

Gauge Freedom in Chiral Gauge Theory with Vacuum Overlap

Dynamical nature of the gauge degrees of freedom and its effect to fermion spectrum are studied at $β=\infty$ for two- and four-dimensional nonabelian chiral gauge theories in the vacuum overlap formalism. It is argued that the disordered gauge degrees of freedom does not contradict to the chiral spectrum of lattice fermion.

hep-lat↗

arXiv1997

The overlap passes a chiral dynamical test in two dimensions

A certain U(1) model in 2 dimensions, describing four right handed unit charged Weyl fermions interacting with one doubly charged left handed Weyl fermion, is exactly soluble and has massless Majorana-Weyl composites. Instanton induced fermion number violation is essential for 't Hooft anomaly consistency. The associated 't Hooft vertex can be analytically computed in the continuum, including finite size corrections. This number is reproduced in a dynamical simulation employing the overlap.

hep-lat↗

arXiv1997

Gauge Freedom in Chiral Gauge Theory with Vacuum Overlap -- Four-dimensional case

Dynamical nature of the gauge degree of freedom and its effect to fermion spectrum are studied for four-dimensional nonabelian chiral gauge theory in the vacuum overlap formulation. The covariant gauge fixing term and the Faddeev-Popov determinant are introduced by hand as a weight for the gauge average. At $β=\infty$, as noticed by Hata some time ago, the model is renormalizable at one-loop and the gauge fixing term turns into an asymptotically free self-coupling of the gauge freedom, even in the presence of the gauge symmetry breaking of the complex phase of chiral determinant. The severe infrared divergence occurs in the perturbation expansion and it prevents local order parameters from emerging. The Foerster-Nielsen-Ninomiya mechanism works in this perturbative framework: the small explicit gauge symmetry breaking term does not affect the above infrared structure. Based on these dynamical features, which is quite similar to the two-dimensional nonlinear sigma model, we assume that the global gauge symmetry does not break spontaneously and the gauge freedom acquires mass dynamically. The asymptotic freedom allows us to tame the gauge fluctuation by approaching the critical point of the gauge freedom without spoiling its disordered nature. Then it is argued that the disordered gauge freedom does not necessarily cause the massless chiral state in the (waveguide) boundary correlation function and that the entire fermion spectrum can be chiral.

hep-lat↗

arXiv1997

Gauge Freedom in Chiral Gauge Theory with Vacuum Overlap -- Two-dimensional case

Dynamical nature of the gauge degree of freedom and its effect to fermion spectrum are studied at $β=\infty$ for two-dimensional nonabelian chiral gauge theory in the vacuum overlap formulation. It is argue that the disordered gauge degree of freedom does not necessarily cause the massless chiral state in the (waveguide) boundary correlation function. An asymptotically free self-coupling for the gauge degree of freedom is introduced by hand at first. This allows us to tame the gauge fluctuation by approaching the critical point of the gauge degree of freedom without spoiling its disordered nature. We examine the spectrum in the boundary correlation function and find the mass gap of the order of the lattice cutoff. There is no symmetry against it. Then we argue that the decoupling of the gauge freedom can occur as the self-coupling is removed, provided that the IR fixed point due to the Wess-Zumino term is absent by anomaly cancellation.

hep-lat↗

arXiv1997

Monte Carlo evaluation of a fermion number violating observable in 2D

We describe in some detail a computer evaluation of a 't Hooft vertex in a two dimensional model using the overlap. The computer result agrees with the known exact continuum value, and in this sense our work is a first successful fully dynamical simulation of a chiral gauge theory on the lattice. We add some new data to numbers obtained earlier and provide a selfcontained description which should make it easy for others to reproduce and follow up on our work.

hep-lat↗

arXiv1994

Boundary condition for Staggered Fermion in Lattice Schrödinger Functional of QCD

The fermionic part of the Schrödinger functional of QCD is formulated in the lattice regularization with the staggered fermion. The boundary condition imposed on the staggered fermion field are examined in terms of the four-component Dirac spinor. The boundary terms are different from those of the Symanzik's theory in the flavor structure due to the species doubling. It is argued that, in the case of the homogeneous Dirichlet boundary condition, surface divergence does not occur if the link variables of gauge field are introduced on the original lattice, not on the blocked one. Its application to the numerical calculation of the running coupling constant in QCD is discussed.

hep-lat↗

arXiv1992

Fermion mass in the Wilson-Yukawa approach for chiral Yukawa theory

We consider a modification of the Wilson-Yukawa model to overcome its difficulty that the fermion mass is not proportional to the Higgs vacuum expectation value. In the modification scalar and fermionic regulator fields are introduced so that all the physical fermion fields possess shift symmetry when the Yukawa coupling vanishes. With the fermionic hopping parameter expansion it is shown that the fermion mass is proportional to the Higgs vacuum expectation value and that the coupling of fermion to the external gauge field can be chiral if the hopping parameter of the scalar regulator field is taken to the critical value.

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