WHAT STRING THEORY HAS TAUGHT US ABOUT THE QUANTUM STRUCTURE OF SPACE-TIME

摘要

String theory is the most widely accepted model for quantum gravity and as such it should give an answer to the fundamental question: what is the nature of quantum space-time? A handle on this question was provided through two of the recent conceptual advances in string theory, the (BFSS-type) matrix models and the AdS/CFT duality. In my talk I'll focus on theeecond and discuss two places where the AdS/CFT duality has shed light on the question posed in the title. In particular I'll focus on a matrix theory formulation I proposed to describe the DLCQ of strings on the AdS geometry, the tiny graviton matrix theory, according to which the quantum structure of the AdS*, x S5 geometry contains two noncommutative fuzzy three spheres as well as a noncommutative Moyal plane We'll argue that the appearance of noncommutative geometries is a generic feature of these matrix theories.