The Supergravity Dual of the BMN Matrix Model

TL;DR

This work constructs a type IIA supergravity dual to the 1/2 BPS vacua of the BMN matrix model by applying a Polchinski-Strassler-type analysis to the near-horizon geometry of $N$ D0 branes. Transverse R-R 6-form and NS-NS 3-form fluxes polarize D0 branes into concentric D2 or NS5 shells, with radii scaling with the carried D0 charge; these fluxes encode the BMN mass terms and Myers term while preserving 16 supersymmetries. In the large-$r$ region, the flux perturbations correspond to the mass deformation and Myers-term physics, whereas near the shells the D2 polarization yields equilibrium radii consistent with the fuzzy-sphere vacua of the BMN model. The analysis also discusses flux-source interactions, the interpolation of the metric/dilaton across regions, and potential generalizations to other plane-wave M(atrix) theories and NS5-polarized duals at strong coupling.

Abstract

We propose type IIA supergravity solutions dual to the 1/2 BPS vacua of the BMN matrix model. These dual solutions are analyzed using the Polchinski-Strassler method and have brane configurations of concentric shells of D2 branes (or NS5 branes) with various radii and D0 charge. These branes can be viewed as polarized from $N$ D0 branes by a transverse R-R magnetic 6-form flux and an NS-NS 3-form flux. In the region far from branes, the solutions reduce to perturbation around the near horizon geometry of $N$ D0 branes, by turning on these R-R and NS-NS fluxes, which are dual to the deformation of the BFSS matrix model by adding mass terms and the Myers term. The solutions with these additional fluxes preserve 16 supersymmetries. We also briefly discuss these fluxes in the possible supergravity duals of M(atrix) theories on less supersymmetric plane-waves.