Monopole Operators and Bulk-Boundary Relation in Holomorphic Topological Theories

Abstract

We study the holomorphic twist of 3d N = 2 supersymmetric field theories, discuss the perturbative bulk local operators in general, and explicitly construct non perturbative bulk local operators for abelian gauge theories. Our construction is verified by matching the character of the algebra with the superconformal index. We test a conjectural relation between the derived center of boundary algebras and bulk algebras in various cases, including Landau-Ginzburg models with an arbitrary superpotential and some abelian gauge theories. In the latter cases, monopole operators appear in the derived center of a perturbative boundary algebra. We briefly discuss the higher structures in both boundary and bulk algebras.

arXiv comment65 pages. Comments are welcome

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• Web of Seiberg-like dualities for 3d $\mathcal{N}=2$ quivers
• Infinite Dimensional Topological-Holomorphic Symmetry in Three-Dimensions
• Line defect half-indices of $SU(N)$ Chern-Simons theories
• Integrable models from 4d holomorphic BF theory