  We perform a general analysis of thin-wall Q-balls in AdS space. We provide
numeric solutions and highly accurate analytic approximations over much of the
parameter space. These analytic solutions show that AdS Q-balls exhibit
significant differences from the corresponding flat space solitons. This
includes having a maximum radius beyond which the Q-balls are unstable to a new
type of state where the Q-ball coexists with a gas of massive particles. The
phase transition to this novel state is found to be a zero-temperature
third-order transition. This, through the AdS/CFT correspondence, has
implications for a scalar condensate in the boundary theory.
