Supergravity, AdS/CFT correspondence, and matrix models

The recent developments towards the possible non-perturbative formulation o f string/M theory using supersymmetric Yang-Mills matrix models (SYMs) are discussed. In the first part, we give a critical review on the status of ou r present understanding, focusing on the connection of the D0-brane matrix models to supergravity and its relevance to the so-called Matrix-theory con jecture. We also discuss some problems concerning the conjectured relation between supergravity in AdS background and SYM fr om the viewpoint of D-bra ne interactions. We present a qualitative argument showing how the boundary condition at AdS boundary dictates the correlators on the large N system o f source D-branes. Then, in the final part, we turn to the question how to formulate the condensation of graviton in matrix models, taking the simples t example of type IIB matrix model. We argue the emergence of a hidden symm etry GL(10, R), beyond the manifest Lorentz symmetry SO(9, 1), by embedding U(N) model into models with higher N and by treating the whole recursive s eries of models simultaneously. This suggests a possible approach toward ba ckground independent formulations of matrix models.