Charge constraint in the Berenstein-Maldacena-Nastase model

I derive a new charge constraint in ₁₆ ¹ -Bogomol’nyi-Prasad-Sommerfield sectors of the Berenstein, Maldacena, and Nastase supersymmetric, gauged UðNÞ matrix quantum mechanics. It was previously shown that the supersymmetric index of the model exhibits an exponential dependence on N² from the vacuum that preserves the full gauge group. I show that the reality of the associated entropy implies that the Cartan of SOð3Þ vanishes for any ₁₆ ¹ -Bogomol’nyi-Prasad-Sommerfield sector with UðNÞ gauge symmetry. The Berenstein-Maldacena-Nastase charge constraint could be useful to determine whether there exists a dual supersymmetric black hole solution asymptoting to a plane-wave background.