Monopole Operators and Bulk-Boundary Relation in Holomorphic Topological Theories

TL;DR

This paper explores the holomorphic twist of 3d N=2 theories, constructing non-perturbative bulk operators, and investigates the relation between boundary and bulk algebras, highlighting the role of monopole operators.

Contribution

It provides explicit constructions of non-perturbative bulk operators and tests a conjecture relating boundary and bulk algebra centers in various models.

Findings

Matching of algebra characters with superconformal index

Identification of monopole operators in boundary algebra centers

Verification of boundary-bulk algebra relations in multiple 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.