Decay widths of three-impurity states in the BMN correspondence

We extend the study of the quantum mechanics of BMN gauge theory to the sector of three scalar impurities at one-loop and all genus. The relevant matrix elements of the non-planar one-loop dilatation operator are computed in the gauge theory basis. After a similarity transform the BMN gauge theory prediction for the corresponding piece of the plane wave string Hamiltonian is derived and shown to agree with light-cone string field theory. In the three-impurity sector single string states are unstable for the decay into two-string states at leading order in g2. The corresponding decay widths are computed