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PreprintCC BY 4.0arXiv

Large-charge ADHM-BMN index matching

  • Sarthak Duary
  • Kangning Liu
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Abstract

We compare the superconformal index of three-dimensional ADHM theory in fixed monopole sectors with the index of the BMN matrix model around fuzzy-sphere vacua. The monopole charges determine the sizes of the fuzzy-sphere blocks, and their multiplicities determine how many identical blocks occur. At a fixed number of fundamental hypermultiplets, we increase all positive monopole charges by the same amount while keeping their differences and multiplicities fixed. After dividing the ADHM index by the contribution of the bare monopole, it agrees order by order with the BMN index in the corresponding limit of large blocks. Fundamental excitations move to arbitrarily high orders in the index expansion, while the upper angular-momentum cutoffs of the BMN harmonics diverge, leaving the same vector and adjoint contribution.

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Cite

BibTeXRIS
BibTeX
@misc{duary2026largecharge,
  title = {{Large-charge ADHM-BMN index matching}},
  author = {Sarthak Duary and Kangning Liu},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.28119},
  eprint = {2609.28119},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.28119},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Large-charge ADHM-BMN index matching
AU  - Sarthak Duary
AU  - Kangning Liu
PY  - 2026
DA  - 2026/09/29
PB  - arXiv
DO  - 10.48550/arxiv.2609.28119
UR  - https://arxiv.org/abs/2609.28119
AB  - We compare the superconformal index of three-dimensional ADHM theory in fixed monopole sectors with the index of the BMN matrix model around fuzzy-sphere vacua. The monopole charges determine the sizes of the fuzzy-sphere blocks, and their multiplicities determine how many identical blocks occur. At a fixed number of fundamental hypermultiplets, we increase all positive monopole charges by the same amount while keeping their differences and multiplicities fixed. After dividing the ADHM index by the contribution of the bare monopole, it agrees order by order with the BMN index in the corresponding limit of large blocks. Fundamental excitations move to arbitrarily high orders in the index expansion, while the upper angular-momentum cutoffs of the BMN harmonics diverge, leaving the same vector and adjoint contribution.
ER  -