  We perform a renormalization group analysis of the non-relativistic
four-boson problem by means of a simple model with pointlike three- and
four-body interactions. We investigate in particular the unitarity point where
the scattering length is infinite and all energies are at the atom threshold.
We find that the four-body problem behaves truly universally, independent of
any four-body parameter. Our findings confirm the recent conjectures of Platter
et al. and von Stecher et al. that the four-body problem is universal, now also
from a renormalization group perspective. We calculate the corresponding
relations between the four- and three-body bound states, as well as the full
bound state spectrum and comment on the influence of effective range
corrections.
