Nested coordinate Bethe wavefunctions from the Bethe/gauge correspondence

Abstract

In [1,2], Nekrasov applied the Bethe/Gauge correspondence to derive the su (2) XXX spin-chain coordinate Bethe wavefunction from the IR limit of a 2D N = (2, 2) supersymmetric A 1 quiver gauge theory with an orbifold-type codimension-2 defect. Later, Bullimore, Kim and Lukowski implemented Nekrasov's construction at the level of the UV A 1 quiver gauge theory, recovered his result, and obtained further extensions of the Bethe/Gauge correspondence [3]. In this work, we extend the construction of the defect to A M quiver gauge theories to obtain the su (M + 1) XXX spin-chain nested coordinate Bethe wavefunctions. The extension to XXZ spin-chain is straightforward. Further, we apply a Higgsing procedure to obtain more general A M quivers and the corresponding wavefunctions, and interpret this procedure (and the Hanany-Witten moves that it involves) on the spin-chain side in terms of Izergin-Korepin-type specializations (and re-assignments) of the parameters of the coordinate Bethe wavefunctions.

A class of partition functions associated with $E_{τ,η}(gl_3)$ by Izergin-Korepin analysis

“…In this paper, we introduced and analyzed partition functions associated with E τ,γ (gl 3 ) which is an elliptic analogue of the one recently introduced by Foda and Manabe [32]. For the analysis, we developed a nested version of the Izergin-Korepin method [38,39] which is a higher rank extension of the method for the wavefunctions of six-vertex type models [60,61].…”

“…The partition functions are explicitly expressed as symmetrization of elliptic multivariable functions over two sets of variables. Multivariable functions which have multiple sets of symmetric variables appear as explicit representations for partition functions of Foda-Manabe type [32]. In the context of quantum integrable models, trigonometric weight functions and elliptic weight functions [22,71,72,73,74,75,76,78], which appear in the recent works of the mathematical formulation of the Bethe/Gauge correspondence [77,79] for example, have also multiple sets of symmetric variables.…”

“…We introduce two types of partition functions in this section: the base partition functions and an elliptic analogue of the partition functions introduced by Foda and Manabe [32] recently.…”

“…Next we introduce a class of partition functions associated with E τ.γ (gl 3 ), which is an elliptic analogue of the one recently introduced by Foda and Manabe [32]. Let us denote T a (z|{z (2) }, {w (1) }|λ)…”

“…See [22,23,24,25,26,27,28,29,30,31] for examples on seminal and recent works on this topic. One of the recent progresses is made by Foda and Manabe [32], which they introduced a new class of partition functions for higher rank rational and trigonometric models, motivated by the Bethe/Gauge correspondence [33,34], and their partition functions seem to deserve further studies.…”