Bethe/Gauge Correspondence for ABCDEFG-type 3d Gauge Theories

In this paper, we give a new effective superpotential that makes clear Bethe/Gauge correspondence between 2d (and 3d) $\text{SO/Sp}$ gauge theories and open $\text{XXX}$ (and $\text{XXZ}$) spin chains with diagonal boundary conditions, and also works in the case of 2d (and 3d) ${\text{BC}}_N$-type gauge theories which is not previously discussed in the literature. Especially, for exceptional Lie algebras ${\text{F}}_4$, ${\text{G}}_2$, we give the effective superpotential and vacuum equations. For ${\text{E}}_{6,7,8}$, we only give theirs effective superpotential for convenience.