Related papers: A Lattice Model for Super LLT Polynomials
We construct lattice actions for a variety of (2,2) supersymmetric gauge theories in two dimensions with matter fields interacting via a superpotential.
We investigate non-perturbative supersymmetry breaking in various models of quantum mechanics, including an interesting class of $PT$-invariant models, using lattice path integrals. These theories are discretized on a temporal Euclidean…
In this work, we construct a new Bailey pairs for the integral pentagon identity in terms of q-hypergeometric functions. The pentagon identity considered here represents equality of the partition functions of a certain three-dimensional…
In this paper, we introduce the super telescoping formula, a natural generalization of well-known telescoping formula. We explore various aspects of the formula including its origin and the telescoping cancellations emerging from symmetric…
We propose a lattice action for two dimensional super Yang-Mills theory with a twisted N=2 supersymmetry. The extended supersymmetry is fully and exactly realized on the lattice. The method employed is quite general and its extension to the…
We develop a general scheme for the use of Fermi operators within the framework of integrable systems. This enables us to read off a fermionic Hamiltonian from a given solution of the Yang-Baxter equation and to express the corresponding…
I review motivations for the study of supersymmetric field theories by lattice techniques. In particular, some of the more interesting potential applications are described. These are models of quantum gravity, that rely on the AdS/CFT…
We present an overview of characteristic identities for Lie algebras and superalgebras. We outline methods that employ these characteristic identities to deduce matrix elements of finite dimensional representations. To demonstrate the…
This paper studies systems of linear difference equations on the lattice $\Z^n$ that are invariant under a finite group of symmetries, and shows that there exist solutions to such systems that are also invariant under this group of…
We provide an introduction to recent lattice formulations of supersymmetric theories which are invariant under one or more real supersymmetries at nonzero lattice spacing. These include the especially interesting case of ${\cal N}=4$ SYM in…
We develop a multicomponent lattice Boltzmann (LB) model for the 2D Rayleigh--Taylor turbulence with a Shan-Chen pseudopotential implemented on GPUs. In the immiscible case this method is able to accurately overcome the inherent numerical…
In the article a classification method for nonlinear integrable equations with three independent variables is discussed based on the notion of the integrable reductions. We call the equation integrable if it admits a large class of…
We investigate a Hamiltonian lattice version of the two-dimensional Wess-Zumino model, with special emphasis to the pattern of supersymmetry breaking. Results are obtained by Quantum Monte Carlo simulations and Density Matrix…
Motivated by lattice mixture identification and grain boundary detection, we present a framework for lattice pattern representation and comparison, and propose an efficient algorithm for lattice separation. We define new scale and shape…
We propose a numerical method of estimating various physical quantities in lattice (supersymmetric) quantum mechanics. The method consists only of deterministic processes such as computing a product of transfer matrix, and has no…
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…
The super-algebraic structure of a generalized version of the Jaynes-Cummings model is investigated. We find that a Z2 graded extension of the so(2,1) Lie algebra is the underlying symmetry of this model. It is isomorphic to the…
We discuss generalizations of some results on lattice polygons to certain piecewise linear loops which may have a self-intersection but have vertices in the lattice $\mathbb{Z}^2$. We first prove a formula on the rotation number of a…
Finite and Infinite-dimensional representations of symmetry algebras play a significant role in determining the spectral properties of physical Hamiltonians. In this paper, we introduce and apply a practical method to construct infinite…
Solutions for all Adler-Bobenko-Suris equations excluding Q4 and several lattice Boussinesq-type equations are reconsidered by employing the Cauchy matrix approach. Through introducing a ``fake'' nonautonomous plane wave factor, we derive…