Related papers: Relationship between various supersymmetric lattic…
The lattice definition of the two-dimensional topological quantum field theory [Fukuma, {\em et al}, Commun.~Math.~Phys.\ {\bf 161}, 157 (1994)] is generalized to arbitrary (not necessarily orientable) compact surfaces. It is shown that…
We apply the SL(2,C) lattice Kac-Moody algebra of Alekseev, Faddeev and Semenov-Tian-Shansky to obtain a new lattice description of the SU(2) chiral model in two dimensions. The system has a global quantum group symmetry and it can be…
We consider supersymmetric conformal quantum field theories (SCFTs) with degrees of freedom labeled by lattice data. We will assume that in terms of the corresponding lattice the interactions are nearest neighbor and exactly marginal. For…
We calculate the low-lying glueball spectrum, some string tensions and some properties of topology and the running coupling for SU(N) lattice gauge theories in 3+1 dimensions. We do so for N = 2,3,...12, using lattice simulations with the…
In the framework of the so called link approach we study exact lattice supersymmetry for the simplest supersymmetric model: N=1 supersymmetry in D=1. The model is described by a lattice with spacing a/2, thus containing twice as many sites…
Analytical and numerical methods are applied to principal chiral models on a two-dimensional lattice and their predictions are tested and compared. New techniques for the strong coupling expansion of SU(N) models are developed and applied…
We construct super Yang-Mills theories with ${\cal N}=2, 4$ supersymmetries on the two-dimensional square lattice keeping one or two supercharges exactly. Along the same line as the previous paper \cite{sugino}, the construction is based on…
We present part of our investigations on two dimensional N=1 and N=2 superconformal field theories. As a direct generalization we consider the SU(2) coset models, in particular their renormalization group properties. A search and possible…
An alternative model to the trivial $\phi^4$-theory of the standard model of weak interactions is suggested, which embodies the Higgs-mechanism, but is free of the conceptual problems of standard $\phi ^4$-theory. We propose a N-component,…
A consistent formulation of a fully supersymmetric theory on the lattice has been a long standing challenge. In recent years there has been a renewed interest on this problem with different approaches. At the basis of the formulation we…
The Wegner $Z_2$ gauge theory-$Z_2$ Ising spin model duality in $(2+1)$ dimensions is revisited and derived through a series of canonical transformations. The Kramers-Wannier duality is similarly obtained. The Wegner $Z_2$ gauge-spin…
Topology and generalized symmetries in the $SU(N)/\mathbb{Z}_N$ gauge theory are considered in the continuum and the lattice. Starting from the $SU(N)$ gauge theory with the 't~Hooft twisted boundary condition, we give a simpler explanation…
A general two-dimensional spin model with U$(N)$ invariance, interpolating between $\CPN$ and ${\rm O}(2N)$ models, is studied in detail in order to illustrate both the general features of the $1/N$ expansion on the lattice and the specific…
I review recent approaches to constructing supersymmetric lattice theories focusing in particular on the concept of topological twisting. The latter technique is shown to expose a nilpotent, scalar supersymmetry which can be implemented…
The origin of the bosonic and fermionic solutions, constructed in [1,2,3], to the symmetry equations corresponding to the two-dimensional bosonic and N=(2|2) supersymmetric Toda lattices is established, and algebras of the corresponding…
The $\mathcal{N}{=}\,2$ supersymmetric hyperbolic Calogero-Sutherland model obtained in arXiv:1902.08023 by gauging the $\mathcal{N}{=}\,2$ superfield matrix system is studied. Classical and quantum $\mathcal{N}{=}\,2$ supersymmetry…
We perform Monte Carlo calculation of correlation functions in 4d N=4 super Yang-Mills theory on R*S^3 in the planar limit. In order to circumvent the well-known problem of lattice SUSY, we adopt the idea of a novel large-N reduction, which…
We construct SU($N$) super Yang-Mills theories with extended supersymmetry on hypercubic lattices of various dimensions keeping one or two supercharges exactly. It is based on topological field theory formulation for the super Yang-Mills…
The second $\mathbb{Z}_{3}$ parafermionic conformal theories are associated with the coset construction $\frac{SU(2)_{k}\times SU(2)_{4}}{SU(2)_{k+4}} $. Solid-on-solid integrable lattice models obtained by fusion of the model based on…
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.…