Bethe/Gauge correspondence for linear quiver theories with ABCD gauge symmetry and spin chains

This note is an extension of [DZ23] there the supersymmetric vacua three-dimensional $\mathcal{N}=2$ gauge theories with matter are shown to be in one-to-one correspondence eigenstate $\text{XXZ}$ integrable spin chain Hamiltonians open boundary conditions. We consider $A_{2}$ quiver theory, which simplest non-trivial and $sl_{3}$ diagonal condition. demonstrate between vacuum equations different groups Bethe Ansatz parameters. Not only that, but we furthermore push forward program general $A_{r}$ theory.