A Charge Constraint in BMN

I derive a new charge constraint that ties the four angular momenta in a $\frac{1}{16}$-BPS sector of the Berenstein, Maldacena, and Nastase (BMN) supersymmetric $U(N)$ matrix quantum mechanics. The result is related to the charge constraint of the $U(N)$, $\mathcal{N}=4$ Super-Yang-Mills (SYM) conformal field theory at large $N$ by identifying three SYM charges with three BMN angular momenta generating $SO(6)$, two equal SYM angular momenta with a BMN generator of $SO(3)$, and scaling $N^2$ by $3$. The BMN charge constraint could be useful to determine whether there exists a dual supersymmetric black hole solution asymptoting to a plane-wave background.