Engineering 3D \(\mathcal{N} = 2\) theories using the quantum affine \(\mathfrak{sl}(2)\) algebra (Q2108818)

This paper studies the vortex partition function and the qq-character in a class of gauge theories with \(\mathcal{N}=2\) supersymmetry defined on the omega-deformed background \(\mathbb{R}^2_{\varepsilon} \times S^1\), and expresses them by a network of intertwiners between modules of the shifted quantum affine \(\mathcal{sl}(2)\) algebra [\textit{D. Hernandez} and \textit{M. Jimbo}, Compos. Math. 148, No. 5, 1593--1623 (2012; Zbl 1266.17010)]. The network involves two types of modules, one of which is a new one of vertex representation. The brane system associated to the network is identified, and the role of shifted quantum algebras in implementing the Higgsing procedure is clarified. The paper also gives a nice overview of the related area in the introduction.