Critical fluctuations and breakdown of the Stokes-Einstein relation in the mode-coupling theory of glasses

We argue that the critical dynamical fluctuations predicted by the mode-coupling theory ( MCT) of glasses provide a natural mechanism to explain the breakdown of the Stokes-Einstein relation. This breakdown, observed numerically and experimentally in a region where MCT should hold, is one of the major difficulties of the theory, for which we propose a natural resolution based on the recent interpretation of the MCT transition as a bona fide critical point with a diverging length scale. We also show that the upper critical dimension of MCT for liquids is dc = 8.