  Motivated by recent experimental results on glassy polymer nanoparticles, we
develop a minimal theoretical framework for the glass transition in spherical
confinement. This is accomplished using our cooperative-string model for
supercooled dynamics, that was successful at recovering the bulk phenomenology
and describing the thin-film anomalies. In particular, we obtain predictions
for the mobile-layer thickness as a function of temperature, and for the
effective glass-transition temperature as a function of the radius of the
spherical nanoparticle - including the existence of a critical particle radius
below which vitrification never occurs. Finally, we compare the theoretical
results to experimental data on polystyrene from the recent literature, and we
discuss the latter.
