Bit Strings from N=4 Gauge Theory

We present an improvement of the interacting string bit theory proposed in hep-th/0206059, designed to reproduce the non-planar perturbative amplitudes between BMN operators in N=4 gauge theory. Our formalism incorporates the effect of operator mixing and all non-planar corrections to the inner product. We use supersymmetry to construct the bosonic matrix elements of the light-cone Hamiltonian to all orders in g_2, and make a detailed comparison with the non-planar amplitudes obtained from gauge theory to order (g_2)^2. We find a precise match.