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 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 Ω-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 N = 4 quiver theories. Examples include line operators that conjecturally create T, Q, and L-operators in integrable spin chains.