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

Abstract

The algebraic engineering technique is applied to a class of 3D $\mathcal{N}=2$ gauge theories on the omega-deformed background ${\mathbb{R}}_{\epsilon }^2\times S^1$. The vortex partition function and the fundamental qq-character are obtained from a network of intertwiners between representations of the shifted (or asymptotic) quantum affine $\mathfrak{sl}(2)$ algebra. This network involves two types of representations, the prefundamental representation of Hernandez-Jimbo, and a new vertex representation acting on a bosonic Fock space. The brane system associated to this network is identified: D3 branes carry the prefundamental module while NS5-branes (+D5) support the Fock module. In the process, we highlight the role of shifted quantum algebras in implementing the Higgsing procedure.

25 pages (v2: minor corrections)

References in corpus (2)

• Flipping the head of T[SU(N)]: mirror symmetry, spectral duality and monopoles
• Reflection states in Ding-Iohara-Miki algebra and brane-web for D-type quiver

Cited by in corpus (3)

• Quantum toroidal algebras and solvable structures in gauge/string theory
• 5d AGT correspondence of supergroup gauge theories from quantum toroidal ${\mathfrak{gl}}_1$
• Gauge origami and quiver W-algebras