  We report the exact calculation of the Fermi-edge singularity exponent for
correlated electrons in one dimension (Luttinger liquid). Focusing on the
special interaction parameter g=1/2, the asymptotic long-time behavior can be
obtained using the Wiener-Hopf method. The result confirms the previous
assumption of an open boundary fixed point. In addition, a dynamic k-channel
Kondo impurity is studied via Abelian bosonization for k=2 and k=4. It is shown
that the corresponding orthogonality exponents are related to the orthogonality
exponent in a Luttinger liquid.
