Glassy dynamics: mean-field `landscape' pictures versus growing length scale scenarii

Abstract

This is a short review on the compatibility between (a) mean-field, mode-coupling theories of the glass transition, where potential energy landscape ideas are natural, and (b) the necessity of describing the slowing down of glassy materials in terms of a growing cooperative length, absent from mean-field descriptions. We summarize some of the outstanding questions that remain before we can say we understand why glasses do not flow.