  Dense assemblies of self-propelled particles undergo a nonequilibrium form of
glassy dynamics. Physical intuition suggests that increasing departure from
equilibrium due to active forces fluidifies a glassy system. We falsify this
belief by devising a model of self-propelled particles where increasing
departure from equilibrium can both enhance or depress glassy dynamics,
depending on the chosen state point. We analyze a number of static and dynamic
observables and suggest that the location of the nonequilibrium glass
transition is primarily controlled by the evolution of two-point static density
correlations due to active forces. The dependence of the density correlations
on the active forces varies non-trivially with the details of the system, and
is difficult to predict theoretically. Our results emphasize the need to
develop an accurate liquid state theory for nonequilibrium systems.
