Higher genus BMN correlators: factorization and recursion relations

Abstract

We systematically study the factorization and recursion relations in higher genus correlation functions of Berenstein–Maldacena–Nastase (BMN) operators in free $\mathcal{N} = 4$ super Yang–Mills theory. These properties were found in a previous paper by the author, and were conjectured to result from the correspondence with type IIB string theory on the infinitely curved pp-wave background, where the strings become effectively infinitely long. Here we push the calculations to higher genus, provide more clarifications and verifications of the factorization and recursion relations. Our calculations provide conjectural indirect tests of the AdS/ CFT correspondence for multi-loop superstring amplitudes of stringy modes.