  We investigate the zero-temperature phase diagram of two-orbital SU(N)
fermionic models at incommensurate filling which are directly relevant to
strontium and ytterbium ultracold atoms loading into a one-dimensional optical
lattice. Using a low-energy approach that takes into account explicitly the
SU(N) symmetry, we find that a spectral gap for the nuclear-spin degrees of
freedom is formed for generic interactions. Several phases with one or two
gapless modes are then stabilized which describe the competition between
different density instabilities. In stark contrast to the N=2 case, no dominant
pairing instabilities emerge and the leading superfluid one is rather formed
from bound states of 2N fermions.
