$\mathfrak{gl}_N$ Higgsed networks

TL;DR

This paper extends Higgsed networks of intertwiners to the quantum toroidal algebra of bN, deriving screening operators for W-algebras and reproducing 3d partition functions on orbifolded backgrounds.

Contribution

It introduces a generalized framework for Higgsed networks in the context of bN quantum toroidal algebra, linking to W-algebras and 3d theories.

Findings

Derived screening operators for W-algebras from bN Higgsed networks.

Reproduced partition functions of 3d theories on orbifolded backgrounds.

Established connections between Higgsed networks, W-algebras, and quantum toroidal algebra.

Abstract

We generalize the framework of Higgsed networks of intertwiners to the quantum toroidal algebra associated to Lie algebra $\mathfrak{gl}_N$. Using our formalism we obtain a systems of screening operators corresponding to W-algebras associated to toric strip geometries and reproduce partition functions of 3d theories on orbifolded backgrounds.