Renormalization group analysis of competing orders and the pairing symmetry in Fe-based superconductors

We analyze antiferromagnetism and superconductivity in novel Fe-based superconductors within the weak-coupling, itinerant model of electron and hole pockets near (0,0) and (\pi,\pi) in the folded Brillouin zone. We discuss the interaction Hamiltonian, the nesting, the RG flow of the couplings at energies above and below the Fermi energy, and the interplay between SDW magnetism, superconductivity and charge orbital order. We argue that SDW antiferromagnetism wins at zero doping but looses to superconductivity upon doping. We show that the most likely symmetry of the superconducting gap is A_{1g} in the folded zone. This gap has no nodes on the Fermi surface but changes sign between hole and electron pockets. We also argue that at weak coupling, this pairing predominantly comes not from a spin fluctuation exchange but from a direct pair hopping between hole and electron pockets.