Related papers: A Lattice Model for Super LLT Polynomials
We survey three methods for proving that the characteristic polynomial of a finite lattice factors over the nonnegative integers and indicate how they have evolved recently. The first technique uses geometric ideas and is based on…
We propose a new lattice superfield formalism in momentum representation which accommodates species doublers of the lattice fermions and their bosonic counterparts as super multiplets. We explicitly show that one dimensional $N=2$ model…
We discuss the motivations, difficulties and progress in the study of supersymmetric lattice gauge theories focusing in particular on ${\cal N}=1$ and ${\cal N}=4$ super Yang-Mills in four dimensions. Brief reviews of the corresponding…
We present a new lattice super Yang-Mills theory and its SUSY transformation. After our formulation of the model in a fundamental lattice, it is extended to the whole lattice with a substructure of modulo 2.
The usual Cauchy matrix approach starts from a known plain wave factor vector $r$ and known dressed Cauchy matrix $M$. In this paper we start from a matrix equation set with undetermined $r$ and $M$. From the starting equation set we can…
We establish a direct connection between the representation theories of Lie algebras and Lie superalgebras (of type A) via Fock space reformulations of their Kazhdan-Lusztig theories. As a consequence, the characters of finite-dimensional…
We construct a lattice model for two-dimensional N=(2,2) supersymmetric QCD (SQCD), with the matter multiplets belonging to the fundamental or anti-fundamental representation of the gauge group U(N) or SU(N). The construction is based on…
We introduce families of two-parameter multivariate polynomials indexed by pairs of partitions $v,w$ -- biaxial double $(\beta,q)$-Grothendieck polynomials -- which specialize at $q=0$ and $v=1$ to double $\beta$-Grothendieck polynomials…
Some particular examples of classical and quantum systems on the lattice are solved with the help of orthogonal polynomials and its connection to continuous models are explored.
We construct a variety of supersymmetric gauge theories on a spatial lattice, including N=4 supersymmetric Yang-Mills theory in 3+1 dimensions. Exact lattice supersymmetry greatly reduces or eliminates the need for fine tuning to arrive at…
A lattice formulation of a three dimensional super Yang-Mills model with a twisted N=4 supersymmetry is proposed. The extended supersymmetry algebra of all eight supercharges is fully and exactly realized on the lattice with a modified…
Matrix-valued Cauchy bi-orthogonal polynomials were proposed in this paper, together with its quasideterminant expression. It is shown that the coefficients in four-term recurrence relation for matrix-valued Cauchy bi-orthogonal polynomials…
The finite Pfaff lattice is given by commuting Lax pairs involving a finite matrix L (zero above the first subdiagonal) and a projection onto Sp(N). The lattice admits solutions such that the entries of the matrix L are rational in the time…
As a prelude to what might be expected as forthcoming breakthroughs in finding new approaches toward solving three-dimensional lattice models in the twenty-first century, we review the exact solutions of two lattice models in three…
Brauer and Thrall conjectured that a finite-dimensional algebra over a field of bounded representation type is actually of finite representation type and a finite-dimensional algebra (over an infinite field) of infinite representation type…
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).
We construct lattice action for five-dimensional maximally supersymmetric Yang-Mills theory. This supersymmetric lattice formulation can be used to explore the non-perturbative regime of the continuum target theory, which has a known…
We consider matrix-model representations of the meander problem which describes, in particular, combinatorics for foldings of closed polymer chains. We introduce a supersymmetric matrix model for describing the principal meander numbers.…
We show that some models with non-local (and non-localizable) interactions have a property, called quasi-locality, which allows for the definition of a transfer matrix. We give the Yang-Baxter equation as a sufficient condition for the…
A lattice model of critical dense polymers is solved exactly for finite strips. The model is the first member of the principal series of the recently introduced logarithmic minimal models. The key to the solution is a functional equation in…