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arXiv · 2609.28119

Equal-GNO Sectors and Fuzzy-Sphere Vacua: Large-Charge ADHM-BMN Index Matching

Sarthak Duary·Kangning Liu
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Abstract

We establish a protected-sector relation between the superconformal index of the three-dimensional ADHM theory and the fixed-vacuum Witten index of BMN matrix quantum mechanics. The comparison selects a positive equal-magnetic-charge sector of the ADHM localization formula and a BMN vacuum made from identical fuzzy-sphere blocks. Equal magnetic charges preserve the complete multiplicity gauge group and make the vector and adjoint determinants independent of the common charge. Fundamental fields instead experience the full monopole background and develop a magnetic gap. In the large-GNO-charge limit, their oscillator determinant decouples from every fixed order of the protected expansion, while the associated vacuum monomial survives and fixes the normalization of the sector. After this normalization, the ADHM matrix integral in the large-GNO-charge limit agrees coefficientwise with the large-block limit of the BMN index. The matching therefore arises from two physically distinct mechanisms: in the large-GNO-charge limit, the fundamental-hypermultiplet excitations become magnetically heavy and decouple on the ADHM side, while in the large-block limit, the finite fuzzy-sphere angular-momentum cutoff is removed on the BMN side, leaving the complete angular tower. We establish the correspondence coefficientwise, distinguish the exact determinant identities from the large-charge asymptotics, and show that the GNO-charge partition becomes, after the M-theory uplift, the distribution of longitudinal momentum among the BMN fuzzy-sphere blocks.

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Sarthak Duary, Kangning Liu. 2026-09-23. Equal-GNO Sectors and Fuzzy-Sphere Vacua: Large-Charge ADHM-BMN Index Matching. https://arxiv.org/abs/2609.28119

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