SYM Description of SFT Hamiltonian in a PP-Wave Background

We compute string field theory Hamiltonian matrix elements and compare them with matrix elements of the dilatation operator in gauge theory. We get precise agreement between the string field theory and gauge theory computations once the correct cubic Hamiltonian matrix elements in string field theory and a particular basis of states in gauge theory are used. We proceed to compute the matrix elements of the dilatation operator to order g 2 in this same basis. This calculation makes a prediction for string field theory Hamiltonian matrix elements to order g 2, which have not yet been computed. However, our gauge theory results precisely match the results of the recent computation by Pearson et al. of the order g 2 Hamiltonian matrix elements of the string bit model.