Ultracold fermions and the SU(N) Hubbard model

We investigate the fermionic SU(N) Hubbard model on the two-dimensional square lattice for weak to moderate interaction strengths using one-loop renormalization group and mean-field methods. For the repulsive case U>0 at half filling and small N the dominant tendency is towards breaking of the SU(N) symmetry. For N>6 staggered flux order takes over as the dominant instability, in agreement with the large-N limit. Away from half filling for N=3 the system rearranges the particle densities such that two flavors remain half filled by cannibalizing the third flavor. In the attractive case and odd N a full Fermi surface coexists with a superconductor in the ground state. These results may be relevant to future experiments with cold fermionic atoms in optical lattices.