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).

N=4 supersymmetric quantum mechanical model is formulated on the lattice. Two
supercharges, among four, are exactly conserved with the help of the cyclic
Leibniz rule without spoiling the locality. In use of the cohomological
argument, any possibl...

We construct a class of quadratic gauge invariant actions for extended string
fields defined on the tensor product of open superstring state space for
multiple open string Neveu-Schwarz (NS) sectors with or without one Ramond (R)
sector. The basic...

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...

Hybrid Monte Carlo on Lefschetz thimbles - A study of the residual sign problem

H. Fujii, D. Honda, M. Kato, Y. Kikukawa, S. Komatsu, T. Sano

We propose a new gauge field theory which is an extension of ordinary string
field theory by assembling multiple state spaces of the bosonic string. The
theory includes higher spin fields in its massless spectrum together with the
infinite tower o...

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...

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...

We show that a-gauge, a class of covariant gauges developed for bosonic open
string field theory, is consistently applied to the closed string field theory.
A covariantly gauge-fixed action of massless fields can be systematically
derived from a-g...

An obstacle to realize supersymmetry on a lattice is the breakdown of Leibniz
rule. We give a proof of a no-go theorem that it is impossible to construct a
lattice field theory in an infinite lattice volume with any nontrivial field
products and d...

A general class of gauges for open string field theory, for which the gauge
fixing condition is given by linear equations with respect to string field, is
investigated in detail. This class of gauges includes almost all known ones
like Siegel gaug...

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...

Prog.Theor.Phys.117:569-587,2007 117(3) 569-587 Mar 2007 [Refereed]

A single-parameter family of covariant gauge fixing conditions in bosonic
string field theory is proposed. It is a natural string field counterpart of
the covariant gauge in the conventional gauge theory, which includes the Landau
gauge as well as...

New gauge fixing condition with single gauge parameter proposed by the
authors is applied to the level truncated analysis of tachyon condensation in
cubic open string field theory. It is found that the only one real non-trivial
extremum persists t...

We propose a new formulation of lattice theory. It is given by a matrix form
and suitable for satisfying Leibniz rule on lattice. The theory may be
interpreted as a multi-flavor system. By realizing the difference operator as a
commutator, we may ...

We re-examine physical state representations in the covariant quantization of
bosonic string. We especially consider one parameter family of gauge fixing
conditions for the residual gauge symmetry due to null states (or BRST exact
states), and obt...

We present a new formulation of the staggered fermion on the D-dimensional
lattice based on the SO(2D) Clifford algebra, which is naturally present in the
action. The action of the massless staggered fermion is invariant under the
discrete rotatio...

Novel approach to superYang-Mills theory on lattice: Exact fermionic symmetry and 'Ichimatsu' pattern

Katsumi Itoh, Mitsuhiro Kato, Hideyuki Sawanaka, Hiroto So, Naoya Ukita

Katsumi Itoh, Mitsuhiro Kato, Hideyuki Sawanaka, Hiroto So, Naoya Ukita

Prog.Theor.Phys. 108 (2002) 363-374 108(2) 363-374 Aug 2002 [Refereed]

We present an entirely new approach towards a realization of the
supersymmetric Yang-Mills theory on the lattice. The action consists of the
staggered fermion and the plaquette variables distributed in the Euclidean
space with a particular pattern...

It is known that the noncommutativity of D-brane coordinate is responsible
for describing the higher-dimensional D-branes in terms of more fundamental
ones such as D-particles or D-instantons, while considering a noncommutative
torus as a target s...

Starting from the primal principle based on the noncommutative nature of
(9+1)-dimensional spacetime, we construct a topologically twisted version of
the supersymmetric reduced model with a certain modification. Our formulation
automatically provi...

Possible Dirichlet boundary states for WZW models with untwisted affine super
Kac-Moody symmetry are classified for all compact simple Lie groups. They are
obtained by inner- and outer-automorphism of the group. D-brane world-volume
turns out to b...

Several examples of similarity transformations connecting two string theories
with different backgrounds are reviewed. We also discuss general structure
behind the similarity transformations from the point of view of the topological
conformal alge...

We study the relation between the black hole and the
Liouville theory. A deformation, which interpolates the BRST operators of both
models, is explicitly constructed. This interpolation is isomorphic, and the
physical spectrum...

A lattice supersymmetric gauge theory would be of vital importance to investigate the physics beyond the standard model. After briefly describing various difficulties encountered in earlier works, we explain our model, which carries some lattice s...