Numerical Renormalization Group Study of Pseudo-Fermion and Slave-Boson   Spectral Functions in the Single Impurity Anderson Model
  We use the numerical renormalization group to calculate the auxiliary spectral functions of the $U=\infty$ Anderson impurity model. The slave--boson and pseudo--fermion spectral functions diverge at the threshold with exponents $\alpha_{b}$ and $\alpha_{f}$ given in terms of the conduction electron phase shifts by the X--ray photoemission and the X--ray absorption exponents respectively. The exact exponents obtained here depend on the impurity occupation number, in contrast to the NCA results. Vertex corrections in the convolution formulae for physical Green's functions are singular at the threshold and may not be neglected in the Fermi liquid regime. 
T. A. Costi, P. Schmitteckert, J. Kroha and P. Woelfle