Line operators in 4d Chern-Simons theory and Cherkis bows

Abstract

We show that the phase spaces of a large family of line operators in 4d Chern-Simons theory with GL_nn gauge group are given by Cherkis bow varieties with nn crosses. These line operators are characterized by Hanany-Witten type brane constructions involving D3, D5, and NS5 branes in an \OmegaΩ-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}=4𝒩=4 quiver theories. Examples include line operators that conjecturally create T, Q, and L-operators in integrable spin chains.