  We consider a three-component Fermi gas that has SU(3) symmetry and is
confined to two dimensions (2D). For realistic cold atomic gas experiments, we
show that the phase diagram of the quasi-2D system can be characterized using
two 2D scattering parameters: the scattering length and the effective range.
Unlike the case in 3D, we argue that three-body bound states (trimers) in the
quasi-2D system can be stable against three-body losses. Using a low-density
expansion coupled with a variational approach, we investigate the fate of such
trimers in the many-body system as the attractive interactions are decreased
(or, conversely, as the density of particles is increased). We find that
remnants of trimers can persist in the form of strong three-body correlations
in the weak-coupling (high-density) limit.
