Mott transition at large orbital degeneracy: Dynamical mean-field theory

We study analytically the Mott transition of the N-orbital Hubbard model using dynamical mean-field theory and a low-energy projection onto an effective Kondo model. It is demonstrated that the critical interaction at which the insulator appears (U-c1) and the one at which the metal becomes unstable (U-c2) have a different dependence on the number of orbitals as the latter becomes large: U(c1)proportional torootN while U(c2)proportional toN. An exact analytical determination of the critical coupling U-c2/N is obtained in the large-N limit. The metallic solution close to this critical coupling has many similarities at low-energy with the results of slave boson approximations, to which a comparison is made. We also discuss how the critical temperature associated with the Mott critical endpoint depends on the number of orbitals.