Extended Supersymmetric Quantum Mechanics of Fierz and Schur Type

Elliptic supersymmetric integrable model and multivariable elliptic functions

We investigate the elliptic integrable model introduced by Deguchi and Martin, which is an elliptic extension of the Perk-Schultz model. We introduce and study a class of partition functions of the elliptic model by using the Izergin-Korepin analysis. We show that the partition functions are expressed as a product of elliptic factors and elliptic Schur-type symmetric functions. This result resembles the recent works by number theorists in which the correspondence between the partition functions of trigonometric models and the product of the deformed Vandermonde determinant and Schur functions …

Airy Point Process via Supersymmetric Lifts

We study the local asymptotics at the edge for particle systems arising from: (i) eigenvalues of sums of unitarily invariant random Hermitian matrices and (ii) signatures corresponding to decompositions of tensor products of representations of the unitary group. Our method treats these two models in parallel, and is based on new formulas for observables described in terms of a special family of lifts, which we call supersymmetric lifts, of Schur functions and multivariate Bessel functions. We obtain explicit expressions for a class of supersymmetric lifts inspired by determinantal formulas for…

自由费米子Schur函数

Free Fermionic Schur Functions

本文引入依赖两组变量和两列参数的自由费米子Schur函数，利用六顶点模型的精化Yang-Baxter方程统一证明超对称Cauchy恒等式及众多经典Schur函数性质。

One-Dimensional Vertex Models Associated with a Class of Yangian Invariant Haldane-Shastry Like Spin Chains

We define a class of $Y(sl_{(m|n)})$ Yangian invariant Haldane-Shastry (HS) like spin chains, by assuming that their partition functions can be written in a particular form in terms of the super Schur polynomials. Using some properties of the super Schur polynomials, we show that the partition functions of this class of spin chains are equivalent to the partition functions of a class of one-dimensional vertex models with appropriately defined energy functions. We also establish a boson-fermion duality relation for the partition functions of this class of supersymmetric HS like spin chains by u…

SCFT/VOA correspondence via $Ω$-deformation

We investigate an alternative approach to the correspondence of four-dimensional $\mathcal{N}=2$ superconformal theories and two-dimensional vertex operator algebras, in the framework of the $Ω$-deformation of supersymmetric gauge theories. The two-dimensional $Ω$-deformation of the holomorphic-topological theory on the product four-manifold is constructed at the level of supersymmetry variations and the action. The supersymmetric localization is performed to achieve a two-dimensional chiral CFT. The desired vertex operator algebra is recovered as the algebra of local operators of the resultin…

The open supersymmetric Haldane-Shastry spin chain and its associated motifs

We study the open version of the su$(m|n)$ supersymmetric Haldane-Shastry spin chain associated to the $BC_N$ extended root system. We first evaluate the model's partition function by modding out the dynamical degrees of freedom of the su$(m|n)$ supersymmetric spin Sutherland model of $BC_N$ type, whose spectrum we fully determine. We then construct a generalized partition function depending polynomially on two sets of variables, which yields the standard one when evaluated at a suitable point. We show that this generalized partition function can be written in terms of two variants of the clas…