  The classical ground states of the SU(4) Heisenberg model on the face
centered cubic lattice constitute a highly degenerate manifold. We explicitly
construct all the classical ground states of the model. To describe quantum
fluctuations above these classical states, we apply linear flavor-wave theory.
At zero temperature, the bosonic flavor waves select the simplest of these
SU(4) symmetry breaking states, the four-sublattice ordered state defined by
the cubic unit cell of the fcc lattice. Due to geometrical constraints, flavor
waves interact along specific planes only, thus rendering the system
effectively two dimensional and forbidding ordering at finite temperatures. We
argue that longer range interactions generated by quantum fluctuations can
shift the transition to finite temperatures.
