Matrix Theory from Holography
Abstract
We propose a setup that embeds Matrix Theory for M-theory into the AdS/CFT correspondence, allowing the former to be tested using the latter. The central claim is a triality among the BMN matrix model of rank m, a large-charge monopole sector of ABJM theory with charge J, and M-theory on the maximally supersymmetric eleven-dimensional pp-wave with a compact lightlike direction. The relevant ABJM limit sends N,k,J→∞ while keeping N/k2 and m=J/k fixed. We provide quantitative evidence for this triality by showing that, in this triple-scaling limit, the ABJM superconformal index agrees precisely with a grand-canonical sum of Witten indices of the U(m) BMN matrix model. This relation also yields a compact grand-canonical expression for the BMN index, which we use to revisit its large-m behavior. Our analytic and numerical results reveal strong boson--fermion cancellations and show no evidence for the previously claimed eO(m2) growth when the BMN charge scales as Q ∼ m2. We further study the correspondence between the BPS cohomologies of the two theories by constructing a letter-level dictionary. This leads to a new notion of BPS fortuity in ABJM theory that survives even at strict N=∞: although the usual fortuity associated with finite-N trace relations disappears in the triple-scaling limit, each fixed-monopole sector is governed by the effective rank m, and finite-m trace relations generate fortuitous states that map directly to fortuitous states of the BMN matrix model. Finally, we discuss connections to related concepts such as large-charge matrix models, open--closed--open triality, and worldline holography.
Related
BibTeX
@misc{komatsu2026matrix,
title = {{Matrix Theory from Holography}},
author = {Shota Komatsu and Eunwoo Lee and Chintan Patel},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.13386},
eprint = {2609.13386},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.13386},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Matrix Theory from Holography
AU - Shota Komatsu
AU - Eunwoo Lee
AU - Chintan Patel
PY - 2026
DA - 2026/09/22
PB - arXiv
DO - 10.48550/arxiv.2609.13386
UR - https://arxiv.org/abs/2609.13386
AB - We propose a setup that embeds Matrix Theory for M-theory into the AdS/CFT correspondence, allowing the former to be tested using the latter. The central claim is a triality among the BMN matrix model of rank m, a large-charge monopole sector of ABJM theory with charge J, and M-theory on the maximally supersymmetric eleven-dimensional pp-wave with a compact lightlike direction. The relevant ABJM limit sends N,k,J→∞ while keeping N/k^2 and m=J/k fixed. We provide quantitative evidence for this triality by showing that, in this triple-scaling limit, the ABJM superconformal index agrees precisely with a grand-canonical sum of Witten indices of the U(m) BMN matrix model. This relation also yields a compact grand-canonical expression for the BMN index, which we use to revisit its large-m behavior. Our analytic and numerical results reveal strong boson--fermion cancellations and show no evidence for the previously claimed e^O(m^2) growth when the BMN charge scales as Q ∼ m^2. We further study the correspondence between the BPS cohomologies of the two theories by constructing a letter-level dictionary. This leads to a new notion of BPS fortuity in ABJM theory that survives even at strict N=∞: although the usual fortuity associated with finite-N trace relations disappears in the triple-scaling limit, each fixed-monopole sector is governed by the effective rank m, and finite-m trace relations generate fortuitous states that map directly to fortuitous states of the BMN matrix model. Finally, we discuss connections to related concepts such as large-charge matrix models, open--closed--open triality, and worldline holography.
ER -