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Engineering 3D \(\mathcal{N} = 2\) theories using the quantum affine \(\mathfrak{sl}(2)\) algebra. (English) Zbl 1516.81118

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 [D. Hernandez and 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.

MSC:

81R15 Operator algebra methods applied to problems in quantum theory
81R50 Quantum groups and related algebraic methods applied to problems in quantum theory
81Q60 Supersymmetry and quantum mechanics
17B37 Quantum groups (quantized enveloping algebras) and related deformations
17B10 Representations of Lie algebras and Lie superalgebras, algebraic theory (weights)
14L17 Affine algebraic groups, hyperalgebra constructions
17B69 Vertex operators; vertex operator algebras and related structures
81V22 Unified quantum theories

Citations:

Zbl 1266.17010
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References:

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