Interacting Double Coset Magnons

We consider the anomalous dimensions of restricted Schur polynomials constructed using n~O(N) complex adjoint scalars Z and m complex adjoint scalars Y. We fix m<<n so that our operators are almost half BPS. At leading order in m/n this system corresponds to a dilute gas of m free magnons. Adding the first correction of order m/n to the anomalous dimension, which arises at two loops, we find non-zero magnon interactions. The form of this new operator mixing is studied in detail for a system of two giant gravitons with four strings attached.