  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 difficulty 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 is d_c=8.
