Matrix Theory from Holography II: Beyond Counting
Abstract
Extending our earlier realization of Matrix Theory for M-theory within AdS/CFT, we propose and test a new triality among a large-charge sector of three-dimensional 𝒩=4 ADHM theory, the BMN matrix model, and lightlike-compactified M-theory on the maximally supersymmetric pp-wave. In an appropriate triple-scaling limit, the superconformal index of ADHM theory becomes the grand-canonical index of the BMN model, with magnetic-flux sectors corresponding to fuzzy-sphere vacua. But the real interest of this new setup is that we can go beyond counting states. Using supersymmetric localization, we show that correlation functions in topological subsectors agree as well, including their nontrivial dependence on the BMN coupling. In each magnetic-flux sector, both the localization measure and the operator insertions can be matched precisely with those of the corresponding BMN vacuum. Our results also point to a deeper connection between monopole bubbling in ADHM theory and instantons in the BMN model. For minuscule monopole charges, ADHM correlators map directly to topological correlators in the trivial BMN vacuum. For non-minuscule charges, monopole bubbling produces additional screened sectors, whose relative weights reproduce the classical actions of BMN instantons. Mirror symmetry offers another perspective on this structure, mapping the monopole operators to Higgs-branch ``winding" operators in the mirror necklace theory. Finally, we discuss a type IIB counterpart, connecting a large-charge sector of four-dimensional ℤK-orbifold quiver theories, the DLCQ of type IIB string theory on the pp-wave, and level-one mass-deformed ABJM theory on ℝt× T2. As a first test, we show that the superconformal index of the orbifold theory reproduces the vacuum degeneracy of the mass-deformed ABJM theory.
Related
- Matrix Theory from Holography
- Matrix Holography on an Optical Lattice
- A Geodesic Route toward Holography beyond AdS: Tessellating the Schwarzschild Black Hole
- Holography and localization in fractional field theory
- Differentiable topology optimization for high-fidelity acoustic holography beyond the thin-element approximation
BibTeX
@misc{komatsu2026matrix,
title = {{Matrix Theory from Holography II: Beyond Counting}},
author = {Shota Komatsu and Eunwoo Lee and Chintan Patel},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.06999},
eprint = {2611.06999},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.06999},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Matrix Theory from Holography II: Beyond Counting
AU - Shota Komatsu
AU - Eunwoo Lee
AU - Chintan Patel
PY - 2026
DA - 2026/11/04
PB - arXiv
DO - 10.48550/arxiv.2611.06999
UR - https://arxiv.org/abs/2611.06999
AB - Extending our earlier realization of Matrix Theory for M-theory within AdS/CFT, we propose and test a new triality among a large-charge sector of three-dimensional 𝒩=4 ADHM theory, the BMN matrix model, and lightlike-compactified M-theory on the maximally supersymmetric pp-wave. In an appropriate triple-scaling limit, the superconformal index of ADHM theory becomes the grand-canonical index of the BMN model, with magnetic-flux sectors corresponding to fuzzy-sphere vacua. But the real interest of this new setup is that we can go beyond counting states. Using supersymmetric localization, we show that correlation functions in topological subsectors agree as well, including their nontrivial dependence on the BMN coupling. In each magnetic-flux sector, both the localization measure and the operator insertions can be matched precisely with those of the corresponding BMN vacuum. Our results also point to a deeper connection between monopole bubbling in ADHM theory and instantons in the BMN model. For minuscule monopole charges, ADHM correlators map directly to topological correlators in the trivial BMN vacuum. For non-minuscule charges, monopole bubbling produces additional screened sectors, whose relative weights reproduce the classical actions of BMN instantons. Mirror symmetry offers another perspective on this structure, mapping the monopole operators to Higgs-branch ``winding" operators in the mirror necklace theory. Finally, we discuss a type IIB counterpart, connecting a large-charge sector of four-dimensional ℤ_K-orbifold quiver theories, the DLCQ of type IIB string theory on the pp-wave, and level-one mass-deformed ABJM theory on ℝ_t× T^2. As a first test, we show that the superconformal index of the orbifold theory reproduces the vacuum degeneracy of the mass-deformed ABJM theory.
ER -