Bulk perturbations of N=2 branes

The evolution of supersymmetric A-type D-branes under the bulk renormalization group flow between two different N=2 minimal models is studied. Using the Landau-Ginzburg description we show that a specific set of branes decouples from the infrared theory, and we make detailed predictions for the behavior of the remaining branes. The Landau-Ginzburg picture is then checked against a direct conformal field theory analysis. In particular we construct a natural index pairing which is preserved by the RG flow, and show that the branes that decouple have vanishing index with the surviving branes.