Supergravity, AdS/CFT Correspondence, and Matrix Models

Abstract

The recent developments towards the possible non-perturbative formulation of 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 our present understanding, focusing on the connection of the D0-brane matrix models to supergravity and its relevance to the so-called Matrix-theory conjecture. We also discuss some problems concerning the conjectured relation between supergravity in AdS background and SYM from the viewpoint of D-brane interactions. We present a qualitative argument showing how the boundary condition at AdS boundary dictates the correlators on the large N system of 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 simplest example of type IIB matrix model. We argue the emergence of a hidden symmetry 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 series of models simultaneously. This suggests a possible approach toward background independent formulations of matrix models.