Bits, matrices and 1/N

We propose a simple string bit formalism for interacting strings in a plane wave background, in terms of supersymmetric quantum mechanics with a symmetric product target-space. We construct the light-cone supersymmetry generators and hamiltonian at finite string coupling. We find a precise match between string amplitudes and the non-planar corrections to the correlation functions of BMN operators computed from gauge theory, and conjecture that this correspondence extends to all orders in perturbation theory. We also give a simple RG explanation for why the effective string coupling is g₂ = J ²/N instead of g_s = g_ym².