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. © 2004 Elsevier B.V. All rights reserved.
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