A Charge Constraint in BMN

TL;DR

This paper derives a new charge constraint in the $rac{1}{16}$-BPS sectors of the BMN matrix model, linking the reality of entropy to the vanishing of a specific charge, with implications for black hole duals.

Contribution

It introduces a novel charge constraint in the BMN model's BPS sectors, connecting entropy reality to gauge symmetry properties and potential black hole solutions.

Findings

The entropy's reality implies the Cartan of SO(3) vanishes.

The charge constraint may help identify dual black hole solutions.

The supersymmetric index shows exponential dependence on N^2.

Abstract

I derive a new charge constraint in $\frac{1}{16}$-BPS sectors of the Berenstein, Maldacena, and Nastase (BMN) supersymmetric, gauged $U(N)$ matrix quantum mechanics. It was previously shown that the supersymmetric index of the model exhibits an exponential dependence on $N^2$ from the vacuum that preserves the full gauge group. I show that the reality of the associated entropy implies that the Cartan of $SO(3)$ vanishes for any $\frac{1}{16}$-BPS sector with $U(N)$ gauge symmetry. The BMN charge constraint could be useful to determine whether there exists a dual supersymmetric black hole solution asymptoting to a plane-wave background.