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A Charge Constraint in BMN

Yoav Zigdon

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.

A Charge Constraint in BMN

Abstract

I derive a new charge constraint in -BPS sectors of the Berenstein, Maldacena, and Nastase (BMN) supersymmetric, gauged matrix quantum mechanics. It was previously shown that the supersymmetric index of the model exhibits an exponential dependence on from the vacuum that preserves the full gauge group. I show that the reality of the associated entropy implies that the Cartan of vanishes for any -BPS sector with 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.

Paper Structure

This paper contains 9 sections, 118 equations, 1 table.

Table of Contents

  1. Introduction
  2. Review of Aspects of BMN
  3. $\mathcal{N}=4$ Relevant Expressions
  4. Calculation
  5. Equal Charges and Angular Potentials
  6. Unequal Charges
  7. More General Entropy and Charge Constraint
  8. Discussion
  9. Various $\frac{1}{16}$-BPS Indices