The Kondo effect, conformal field theory and fusion rules

In an earlier paper, a relationship was established between the Kondo effect and conformal field theory (CFT) with Kac-Moody (KM) symmetry. Here, we study the case of k degenerate bands, corresponding to a level-k KM algebra, in more detail. At the low-temperature fixed point, the Kac-Moody currents absorb the impurity spin (of size s). We hypothesize that the details of this process are governed by the standard KM fusion rules, the analogue of addition of angular momentum in CFT, and show that this leads to a Fermi liquid and to the expected π/2 phase shift when s ⩾ k/2