ADHM Wilson line defect indices

TL;DR

This paper derives exact formulas for Wilson line defect correlators in 3d $ ext{N}=4$ $U(N)$ ADHM theories, revealing algebraic relations and connecting to gravity dual spectra in M2-brane SCFTs.

Contribution

It provides novel closed-form expressions and algebraic relations for line defect correlators using Hall-Littlewood expansion, Fermi-gas, and residue methods.

Findings

Exact correlator formulas for Wilson lines in fundamental and symmetric reps

Algebraic relations among line defect correlators

Large N limit yields gravity spectrum indices

Abstract

The Coulomb and Higgs indices of the 3d $\mathcal{N}=4$ $U(N)$ ADHM theories can be decorated by line defect operators as the line defect correlators. We obtain exact closed-form expressions and various non-trivial algebraic relations for the correlators of the Wilson lines in the fundamental and (anti)symmetric representations by means of the Hall-Littlewood expansion, the Fermi-gas method and the residue calculation. From the large $N$ limit of the correlators we obtain the single particle gravity indices which are expected to encode the spectra of fluctuation modes on the gravity duals of line operators in M2-brane SCFTs.