Dynamics on the way to forming glass: bubbles in space-time

We review a theoretical perspective of the dynamics of glass-forming liquids and the glass transition, a perspective developed during this past decade based on the structure of trajectory space. This structure emerges from spatial correlations of dynamics that appear in disordered systems as they approach nonergodic or jammed states. It is characterized in terms of dynamical heterogeneity, facilitation, and excitation lines. These features are associated with a newly discovered class of nonequilibrium phase transitions. Equilibrium properties have little, if anything, to do with it. The broken symmetries of these transitions are obscure or absent in spatial structures, but they are vivid in space-time (i.e., trajectory space). In our view, the glass transition is an example of this class of transitions. The basic ideas and principles we review were originally developed through the analysis of idealized and abstract models. Nevertheless, the central ideas are easily illustrated with reference to molecular dynamics of more realistic atomistic models, and we use that illustrative approach here.