  In the limit of perfect nesting, the physics of iron-pnictides is governed by
the density wave formation at the zone-edge vector M. At high energies, various
spin- (SDW), charge- (CDW), orbital/pocket- (PDW) density waves, and their
linear combinations, all appear equally likely, unified within the unitary
order parameter of U(4)XU(4) symmetry. Nesting imperfections and low-energy
interactions reduce this symmetry to that of real materials. Nevertheless, the
generic ground state preserves a distinct signature of its highly symmetric
origins: a SDW along one axis of the iron lattice is predicted to coexist with
a perpendicular PDW, accompanied by weak charge currents. This "hidden" order
induces the structural transition in our theory, naturally insures T_s >= T_N,
and leads to orbital ferromagnetism and other observable consequences.
