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 $N,k,J\to\infty$ 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 $Q \sim m^2$. 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 $N=\infty$: 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.