Superstring Interactions in a pp-wave Background

We construct light-cone gauge superstring field theory in a pp-wave background with Ramond-Ramond flux. The leading term in the interaction Hamiltonian is determined up to an overall function of $p^+$ by requiring closure of the pp-wave superalgebra. The bosonic and fermionic Neumann matrices for this cubic vertex are derived, as is the interaction point operator. We comment on the development of a $1/\mu p^+$ expansion for these results.