This analysis reveals the role of giant gravitons in 3D ADHM theories, suggesting links to Kac-Moody algebras and W-algebras.
We examine the giant graviton expansions of the Higgs indices for the 3d N=4 $U(N)$ ADHM theories with l fundamental hypermultiplets. The indices for the M5-brane giant gravitons of wrapping number m appearing in the expansions consist of the contributions that generalize the characters of the W-algebra W(gl(m)) and those which realize the characters of the affine Kac-Moody algebras of type Aₗ₋₁. Also we confirm that the inverse giant graviton expansions of the resulting M5-brane indices consistently reproduce the Higgs indices.
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Hayashi et al. (2025) studied this question.
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