BMN-like Matrix Models

TL;DR

This paper proposes a family of matrix quantum mechanical models that are conjectured to be holographically dual to certain M-theory backgrounds, extending the BMN matrix model framework to new geometries.

Contribution

It introduces a new class of matrix models derived from superconformal field theories, generalizing the BMN model to pp-wave backgrounds from AdS$_4$×X$_7$.

Findings

Conjecture of holographic duality between matrix models and M-theory backgrounds.

Discussion of supersymmetric black objects and horizon bounds in pp-wave backgrounds.

Connection of matrix models to dimensional reduction of superconformal field theories.

Abstract

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 $N$.