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The Supergravity Duals of the BMN Matrix Model

We provide a holographic description of the BMN matrix model and its 1/2 BPS vacua, e.g. the concentric fuzzy spheres, by dual IIA supergravity solutions. We apply the Polchinski-Strassler method to construct our solutions, due to the similarity of the vacuum structure of this model and the N = 1∗ theory. The dual solutions have brane configurations which are concentric shells of S-wrapped D2 branes with various radii proportional to their D0 charges, or alternatively, concentric NS5 branes with D0 charges, in different regimes of parameters. In our solutions, there are transverse R-R magnetic 6-form flux and NS-NS 3-form flux that polarize N D0 branes to various spherical D2 or NS5 branes carrying fractions of the total D0 charge N . In the region far from all branes, our solutions describe fluctuations around the near horizon geometry of N D0 branes, in terms of these additional 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 propose the supergravity duals of matrix theories on less supersymmetric plane-wave backgrounds. ∗hailin@princeton.edu