  Testing the BMN correspondence at non-zero string coupling g_s requires a
one-loop string field theory calculation. At order g_s^2, matrix elements of
the light-cone string field theory Hamiltonian between single-string states
receive two contributions: the iterated cubic interaction, and a contact term
{Q, Q} whose presence is dictated by supersymmetry. In this paper we calculate
the leading large mu p^+ alpha' contribution from both terms for the set of
intermediate states with two string excitations. We find precise agreement with
the basis-independent order g_2^2 results from gauge theory.
