  Exact critical exponents of the Green functions for pseudo-fermions and slave
bosons in the SU($N$) Anderson model with $U\rightarrow\infty$ are obtained by
using the Bethe ansatz solution and boundary conformal field theory. They are
evaluated exactly for mixed valence systems and Kondo systems with crystalline
fields. The results agree with the prediction of Menge and M\"uller-Hartmann,
which coincide with those of the X-ray problem. Some implication of our results
in one-dimensional chiral systems is also discussed.
