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 $g=1/2\mathrm{}$, 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 $k=2\mathrm{}$ and $k=4\mathrm{}$. It is shown that the corresponding orthogonality exponents are related to the orthogonality exponent in a Luttinger liquid.

• Received 27 February 1997

DOI:https://doi.org/10.1103/PhysRevB.56.1153