  We report the results of a parquet renormalization group (RG) study of
competing instabilities in the full 2D four pocket, three orbital low-energy
model for iron-based superconductors. We derive and analyze the RG flow of the
couplings, which describe all symmetry-allowed interactions between low-energy
fermions. Despite that the number of the couplings is large, we argue that
there are only two stable fixed trajectories of the RG flow and one weakly
unstable fixed trajectory with a single unstable direction. Each fixed
trajectory has a finite basin of attraction in the space of initial system
parameters. On the stable trajectories, either interactions involving only
$d_{xz}$ and $d_{yz}$ or only $d_{xy}$ orbital components on the electron
pockets dominate, while on the weakly unstable trajectory interactions
involving $d_{xz}$ ($d_{yz}$) and $d_{xy}$ orbital states on the electron
pockets remain comparable. The behavior along the two stable fixed trajectories
has been analyzed earlier [A.V. Chubukov, M. Khodas, and R.M. Fernandes,
arXiv:1602.05503]. Here we focus on the system behavior along the weakly
unstable trajectory and apply the results to FeSe. We find, based on the
analysis of susceptibilities along this trajectory, that the leading
instability upon lowering the temperature is towards a {\it three-component}
d-wave orbital nematic order. Two components are the differences between
fermionic densities on $d_{xz}$ and $d_{yz}$ orbitals on hole pockets and on
electron pockets, and the third one is the difference between the densities of
$d_{xy}$ orbitals on the two electron pockets. We argue that this order is
consistent with the splitting of band degeneracies, observed in recent
photoemission data on FeSe by A. Fedorov et al [arXiv:1606.03022].

Strongly Correlated Electrons