Logarithmic corrections in quantum impurity problems

The effect of a bulk marginal operator on boundary critical phenomena in two space-time dimensions is considered. The particular case of an open S = 1/2 antiferromagnetic Heisenberg chain, corresponding to a Wess-Zumino-Witten nonlinear sigma model, is solved. In this case, the required renormalization group coefficient is associated with a novel operator product expansion in which three operators approach the same point. Resulting logarithmic corrections occurring in finite-size calculations and nuclear magnetic resonance experiments are discussed.