Higher Genus BMN Correlators: Factorization and Recursion Relations

TL;DR

This paper investigates the factorization and recursion relations in higher genus BMN correlators within free N=4 super Yang-Mills theory, offering insights into the AdS/CFT correspondence and multi-loop superstring amplitudes.

Contribution

It extends previous work by systematically analyzing higher genus correlation functions, providing new verifications and conjectural tests of the AdS/CFT correspondence.

Findings

Confirmation of factorization and recursion relations at higher genus

Support for the correspondence with type IIB string theory on pp-wave backgrounds

Indirect tests of multi-loop superstring amplitude conjectures

Abstract

We systematically study the factorization and recursion relations in higher genus correlation functions of BMN (Berenstein-Maldacena-Nastase) operators in free 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.