PROGRESS OF THEORETICAL AND EXPERIMENTAL PHYSICS 2019(6) 063B04 Jun 2019 [Refereed]

We study a cyclic Leibniz rule, which provides a systematic approach to
lattice supersymmetry, using a numerical method with a transfer matrix. The
computation is carried out in N=2 supersymmetric quantum mechanics with the
phi^6-interaction for w...

PROGRESS OF THEORETICAL AND EXPERIMENTAL PHYSICS 2018(12) 121B01 Dec 2018 [Refereed]

We construct N=2 supersymmetric SYK model on one-dimensional (euclidean time)
lattice. One nilpotent supersymmetry is exactly realized on the lattice in use
of the cyclic Leibniz rule (CLR).

JOURNAL OF HIGH ENERGY PHYSICS 1305 089 Mar 2013 [Refereed]

It is old folklore that the violation of Leibniz rule on a lattice is an
obstruction for constructing a lattice supersymmetric model. While it is still
true for full supersymmetry, we show that a slightly modified form of the
Leibniz rule, which w...

JOURNAL OF HIGH ENERGY PHYSICS 0805(5) 057 May 2008 [Refereed]

We study a product rule and a difference operator equipped with Leibniz rule
in a general framework of lattice field theory. It is shown that the difference
operator can be determined by the product rule and some initial data through
the Leibniz r...

PROGRESS OF THEORETICAL PHYSICS 117 715-728 2007 [Refereed]

To obtain a light mode in two-dimensional staggered fermions, we introduce
four new local operators keeping the rotational invariance for a staggered
Dirac operator. To split masses of tastes, three cases are considered. The mass
matrix and the pr...

PROGRESS OF THEORETICAL PHYSICS 116 197-215 Apr 2006 [Refereed]

We construct a lattice Dirac operator of overlap type that describes the
propagation of a Dirac fermion in an external gravitational field. The local
Lorentz symmetry is manifestly realized as a lattice gauge symmetry, while it
is believed that th...

PROGRESS OF THEORETICAL PHYSICS 115 467-471 2006 [Refereed]

A zero-dimensional analogue of Witten's global gauge anomaly is considered.
For example, a zero-dimensional reduction of the two-dimensional
Yang-Mills theory with a single Majorana-Weyl fermion in the fundamental
representation suffers ...

We propose a lattice model of supersymmetric complex quantum mechanics which
realizes the non-renormalization theorem on a lattice. In our lattice model,
the Leibniz rule in the continuum, which cannot hold on a lattice due to a
no-go theorem, is ...

For the purpose of constructing supersymmetric(SUSY) theories on lattice, we
propose a new type relation on lattice -cyclic Leibniz rule(CLR)- which is
slightly different from an ordinary Leibniz rule. Actually, we find that CLR
can enlarge the nu...

We introduce a 4-dimensional cutoff in the scenario of gauge-Higgs
unification to control the ultraviolet behavior. A one-loop effective potential
for a Higgs field and the Higgs mass are obtained with the cutoff. We find an
{\it interrelation} be...

In a finite volume system, we prove a no-go theorem on a Leibniz rule with a
care of locality argument on latttice. The new possibility on the Leibniz rule
solutions on lattice is discussed. Although the new solution admits a local
difference oper...

In an SU(2) lattice gauge theory with a Z2 orbifolded extra dimension, the
new symmetry which is called as a stick symmetry is useful in understanding the
bulk transition. We discuss the relation with the Fradkin-Shenker's phase
diagram as well. A...