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

Abstract

This note is an extension of [DZ23] there the supersymmetric vacua of three-dimensional $\mathcal{N}=2$ gauge theories with matter are shown to be in one-to-one correspondence with the eigenstate of $\text{XXZ}$ integrable spin chain Hamiltonians with open boundary conditions. We consider the $A_2$ quiver gauge theory, which is the simplest non-trivial quiver gauge theory, and $s{l}_3$ open $\text{XXZ}$ spin chain with diagonal boundary condition. We demonstrate the correspondence between the vacuum equations of different gauge groups and Bethe Ansatz equations with different boundary parameters. Not only that, but we furthermore push forward the program to the general $A_r$ quiver gauge theory.

30 pages,0 figures, v2: added a subsection in section 4 and fixed typos, accepted by NPB

References in corpus (3)

• Pseudo-differential equations, and the Bethe Ansatz for the classical Lie algebras
• Higgs Bundles, Gauge Theories and Quantum Groups
• Bethe/Gauge Correspondence for ABCDEFG-type 3d Gauge Theories