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arXiv · 2609.07872

ABJM/BMN Index Matching in the Plane-Wave Limit

Chi-Ming Chang·Kangning Liu
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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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Chi-Ming Chang, Kangning Liu. 2026-09-07. ABJM/BMN Index Matching in the Plane-Wave Limit. https://arxiv.org/abs/2609.07872

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