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

TL;DR

This paper establishes a new superpotential framework that clarifies the Bethe/Gauge correspondence for various 2d and 3d gauge theories, including exceptional Lie algebras, extending previous results to new cases.

Contribution

It introduces an effective superpotential that links 2d/3d SO/Sp gauge theories with open XXX/XXZ spin chains, including previously unaddressed BC_N and exceptional Lie algebra cases.

Findings

Superpotential explicitly constructed for F4 and G2 Lie algebras.

Vacuum equations derived for E6, E7, E8 Lie algebras.

Extended Bethe/Gauge correspondence to BC_N-type theories.

Abstract

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.