Wilson's numerical renormalization group and AdS_3 geometry

Abstract

We discuss the relation between the Wilson's numerical renormalization group(NRG) for the Kondo impurity problem and a field theory in the background AdS_3 space time, where the radial coordinate plays a role of the controlling parameter of the effective mass scale. We find that the Wilson NRG can be described by the boundary Rindler field and then the cutoff parameter \lambda of the Wilson NRG is related to the AdS radius L through \lambda = 2k_F/\omega L, where k_F is the effective Fermi wave number. It is also found that the Rindler space is discretized with the lattice space of a=\pi/k_F.