Overscreened multi-channel SU(N) Kondo model : large-N solution and Conformal Field Theory

The multichannel Kondo model with SU(N) spin symmetry and SU(K) channel symmetry is considered. The impurity spin is chosen to transform as an antisymmetric representation of SU(N), corresponding to a fixed number of Abrikosov fermions $\sum_{\alpha}f_{\alpha}^{\dagger}f_{\alpha}=Q$. For more than one channel (K>1), and all values of N and Q, the model displays non-Fermi behaviour associated with the overscreening of the impurity spin. Universal low-temperature thermodynamic and transport properties of this non-Fermi liquid state are computed using conformal field theory methods. A large-N limit of the model is then considered, in which K/N and Q/N are held fixed. Spectral densities satisfy coupled integral equations in this limit, corresponding to a (time-dependent) saddle-point. A low frequency, low-temperature analysis of these equations reveals universal scaling properties in the variable $\omega/T$, also predicted from conformal invariance. The universal scaling form is obtained analytically and used to compute the low-temperature universal properties of the model in the large-N limit, such as the T=0 residual entropy and residual resistivity, and the critical exponents associated with the specific heat and susceptibility. The connections with the ``non-crossing approximation'' and the previous work of Cox and Ruckenstein are discussed.