The single-sum giant graviton expansion of ADHM Higgs indices is proposed to encode, in two fugacity limits, the vacuum characters of the affine Kac-Moody algebras \ hat su(l)_1^{\ times m} and \ hat su(l)_m.
ADHM Wilson line defect indices
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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.
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Kac-Moody algebras from M5-giants
The single-sum giant graviton expansion of ADHM Higgs indices is proposed to encode, in two fugacity limits, the vacuum characters of the affine Kac-Moody algebras \ hat su(l)_1^{\ times m} and \ hat su(l)_m.