ABJM/BMN Index Matching in the Plane-Wave Limit

Abstract

We establish coefficientwise equality between the refined supersymmetric indices of ABJM theory and the BMN matrix model in the plane-wave limit at every fixed positive Chern-Simons level k. For multi-membrane families with fixed multiplicities, and hence fixed finite ABJM gauge rank, the equality holds as all longitudinal momenta tend to infinity with their pairwise differences fixed. Scalar-dressed equal-flux ABJM monopoles correspond to BMN vacua of fuzzy-sphere membranes: multiplicities count coincident membranes, whereas flux magnitudes give the momentum per membrane along the M-theory circle. At the index level, the associated Higgs residues yield a diagonal-holonomy integral for the ABJM plane-wave contribution, whose monopole-harmonic kernel agrees with the BMN matrix-harmonic kernel up to the finite BMN upper-spin cutoff. At finite momentum, the full index difference splits into the non-plane-wave remainder and the harmonic tail above this cutoff. Increasing k shifts the former to higher fugacity grade without changing the surviving kernel or the cutoff contribution. This gives a coefficientwise, multi-membrane extension of the earlier single-membrane index relation.

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BibTeX RIS

BibTeX

@misc{chang2026abjmbmn,
  title = {{ABJM/BMN Index Matching in the Plane-Wave Limit}},
  author = {Chi-Ming Chang and Kangning Liu},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2609.07872},
  eprint = {2609.07872},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.07872},
}

RIS

TY  - UNPB
TI  - ABJM/BMN Index Matching in the Plane-Wave Limit
AU  - Chi-Ming Chang
AU  - Kangning Liu
PY  - 2026
DA  - 2026/10/12
PB  - arXiv
DO  - 10.48550/arxiv.2609.07872
UR  - https://arxiv.org/abs/2609.07872
AB  - We establish coefficientwise equality between the refined supersymmetric indices of ABJM theory and the BMN matrix model in the plane-wave limit at every fixed positive Chern-Simons level k. For multi-membrane families with fixed multiplicities, and hence fixed finite ABJM gauge rank, the equality holds as all longitudinal momenta tend to infinity with their pairwise differences fixed. Scalar-dressed equal-flux ABJM monopoles correspond to BMN vacua of fuzzy-sphere membranes: multiplicities count coincident membranes, whereas flux magnitudes give the momentum per membrane along the M-theory circle. At the index level, the associated Higgs residues yield a diagonal-holonomy integral for the ABJM plane-wave contribution, whose monopole-harmonic kernel agrees with the BMN matrix-harmonic kernel up to the finite BMN upper-spin cutoff. At finite momentum, the full index difference splits into the non-plane-wave remainder and the harmonic tail above this cutoff. Increasing k shifts the former to higher fugacity grade without changing the surviving kernel or the cutoff contribution. This gives a coefficientwise, multi-membrane extension of the earlier single-membrane index relation.
ER  -

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