  We study the effect of confinement on glassy liquids using Random First Order
Transition theory as framework. We show that the characteristic length-scale
above which confinement effects become negligible is related to the
point-to-set length-scale introduced to measure the spatial extent of amorphous
order in super-cooled liquids. By confining below this characteristic size, the
system becomes a glass. Eventually, for very small sizes, the effect of the
boundary is so strong that any collective glassy behavior is wiped out. We
clarify similarities and differences between the physical behaviors induced by
confinement and by pinning particles outside a spherical cavity (the protocol
introduced to measure the point-to-set length). Finally, we discuss possible
numerical and experimental tests of our predictions.
