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 support this triality by showing that the ABJM superconformal index in this limit agrees precisely with a grand-canonical sum of Witten indices of the U(m) BMN matrix model, and by formulating a dictionary between dressed ABJM monopoles and BMN excitations.
