BMN-like Matrix Models

We conjecture a family of matrix quantum mechanical models that are holographically dual to discrete light-cone quantization of M-theory in pp-wave-like backgrounds. These backgrounds can be obtained from a Penrose limit of AdS$_4\times X_7$, where $X_7$ is Einstein. The matrix models arise from a classically consistent dimensional reduction of the UV Lagrangians of $\mathcal{N}=1$ superconformal field theories, in close analogy with how the BMN matrix model is obtained by dimensional reduction from $\mathcal{N}=4$ super Yang-Mills theory. We also discuss about supersymmetric black objects in pp-wave background by studying the Witten index and speculate that the area of the horizon is bounded from above for a fixed $N$.