Related papers: Supersymmetric Polychronakos Spin Chain: Motif, Di…
In this article we consider the cycle structure of compositions of pairs of involutions in the symmetric group S_n chosen uniformly at random. These can be modeled as modified 2-regular graphs, giving rise to exponential generating…
The chiral structure of supersymmetric particle couplings involving third generation Standard Model fermions depends on left-right squark and slepton mixings as well as gaugino-higgsino mixings. The shapes and intercorrelations of invariant…
The purpose of this article is the study of the symmetries in a circular and linear harmonic oscillator chains system, and consequently use them as a means to find the eigenvalues of these configurations. Furthermore, a hidden…
This paper investigates stochastic finite matrices and the corresponding finite Markov chains constructed using recurrence matrices for general families of orthogonal polynomials and multiple orthogonal polynomials. The paper explores the…
We study a spectral problem related to the finite-dimensional characters of the groups $Sp(2N)$, $SO(2N+1)$, and $SO(2N)$, which form the classical series $C$, $B$, and $D$, respectively. The irreducible characters of these three series are…
Using results on topological line defects of 4D Chern-Simons theory and the algebra/cycle homology correspondence in complex surfaces $\mathcal{S}$ with ADE singularities, we study the graded properties of the $sl(m|n)$ chain and its…
This article studies the inhomogeneous geometric polynuclear growth model, the distribution of which is related to Schur functions. We explain a method to derive its distribution functions in both space-like and time-like directions,…
We introduce and study multiple partition structures which are sequences of probability measures on families of Young diagrams subjected to a consistency condition. The multiple partition structures are generalizations of Kingman's…
We discuss relation between the cluster integrable systems and spin chains in the context of their correspondence with 5d supersymmetric gauge theories. It is shown that $\mathfrak{gl}_N$ XXZ-type spin chain on $M$ sites is isomorphic to a…
We do a semiclassical analysis for two or three spins which are coupled antiferromagnetically to each other. The semiclassical wave functions transform correctly under permutations of the spins if one takes into account the Wess-Zumino term…
We use the 5-sphere partition functions of supersymmetric Yang-Mills theories to explore the (2,0) superconformal theory on S^5 x S^1. The 5d theories can be regarded as Scherk-Schwarz reductions of the 6d theory along the circle. In a…
We calculate the spin and charge dynamical susceptibilities of a strongly correlated impurity model in a renormalised perturbation theory. The irreducible for vertices for the quasiparticle scattering are deduced from the renormalised…
Theory of motivic superpolynomials is developed, including its extension to algebraic links colored by rows, relations to $L$-functions of plane curve singularities, the justification of the motivic versions of Weak Riemann Hypothesis, and…
Skew orthogonal polynomials arise in the calculation of the $n$-point distribution function for the eigenvalues of ensembles of random matrices with orthogonal or symplectic symmetry. In particular, the distribution functions are completely…
In this paper, we explore supersymmetric and 2d analogs of the SYK model. We begin by working out a basis of (super)conformal eigenfunctions appropriate for expanding a four-point function. We use this to clarify some details of the 1d…
Some of the recent important developments in understanding string/ gauge dualities are based on the idea of highly symmetric motion of ``string solitons'' in $AdS_5\times S^5$ geometry originally suggested by Gubser, Klebanov and Polyakov.…
If signals suggesting supersymmetry (SUSY) are discovered at the LHC then it will be vital to measure the spin of the new particles to demonstrate that they are indeed the predicted super-partners. A method is discussed by which the spins…
We investigate various aspects of higher-spin anti-de Sitter supergravity in three dimensions as described by Chern-Simons theory based on the finite-dimensional superalgebra sl(N |N - 1), with the particular case of N = 3 as our prime…
Dynamical properties, such as dynamical spin and charge structure factors and single-particle spectral functions, are studied for the one-dimensional supersymmetric t-J model with inverse-square interaction. Exact diagonalization and the…
We study polarized deep inelastic scattering of charged leptons from spin-$1/2$ hadrons at low values of the Bjorken parameter and large 't Hooft coupling in terms of the gauge/string theory duality. We calculate the structure functions…