Quantum integrability from non-simply laced quiver gauge theory

We consider the compactifcation of 5d non-simply laced fractional quiver gauge theory constructed in https://arxiv.org/abs/1705.04410. In contrast to the simply laced quivers, here two $\Omega$-background parameters play different roles, so that we can take two possible Nekrasov–Shatashvili limits. We demonstrate how different quantum integrable systems can emerge from these two limits, using $B{C}_2$-quiver as the simplest illustrative example for our general results. We also comment possible connections with compactified 3d non-simply laced quiver gauge theory.