EXACT FERMI-EDGE SINGULARITY EXPONENT IN A LUTTINGER LIQUID

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