Line Operators in 4d Chern-Simons Theory and Cherkis Bows

TL;DR

This paper links phase spaces of line operators in 4d Chern-Simons theory with Cherkis bow varieties, using brane constructions, and explores their relation to integrable spin chain operators.

Contribution

It establishes a novel connection between line operators in 4d Chern-Simons theory and Cherkis bow varieties, expanding understanding of their phase spaces and integrable models.

Findings

Phase spaces are given by Cherkis bow varieties with n crosses.

Line operators relate to vacuum moduli spaces of 3d N=4 quiver theories.

Examples include line operators conjecturally creating T, Q, and L-operators.

Abstract

We show that the phase spaces of a large family of line operators in 4d Chern-Simons theory with $\text{GL}_n$ gauge group are given by Cherkis bow varieties with $n$ crosses. These line operators are characterized by Hanany-Witten type brane constructions involving D3, D5, and NS5 branes in an $\Omega$-background. Linking numbers of the five-branes and mass parameters for the D3 brane theories determine the phase spaces and in special cases they correspond to vacuum moduli spaces of 3d $\mathcal{N}=4$ quiver theories. Examples include line operators that conjecturally create T, Q, and L-operators in integrable spin chains.