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 ${\text{GL}}_n$ 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.

42+5 pages. v4: Corrected several typos, added some references and clarifying comments based on referee report

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Cited by in corpus (1)

• Elliptic Stable Envelopes for Certain Non-Symplectic Varieties and Dynamical $R$-Matrices for Superspin Chains from the Bethe/Gauge Correspondence