PP-wave/Yang-Mills Correspondence: An Explicit Check

TL;DR

The paper provides a concrete test of the pp-wave BMN duality by deriving the cubic light-cone Hamiltonian for the dilaton-axion sector in IIB supergravity on a pp-wave, fixing the $p^+$-dependent normalization via comparison with light-cone string field theory. It shows that, after appropriate field redefinitions and zero-mode treatment, the cubic interactions align with flat-space results up to Lorentz-invariance-restoring terms, and computes explicit matrix elements for three chiral primaries. By matching these results with a dual Yang-Mills calculation, it confirms agreement (up to normalization) with a specific YM prediction for the proposed chiral-primary processes, thereby providing a nontrivial check of the pp-wave/correspondence at the interaction level. The work also highlights how two $SO(4)$ sectors contribute differently on the YM side, suggesting refinements in the dictionary between pp-wave string dynamics and large-$N$ gauge theory in this limit.

Abstract

We present an explicit evidence that shows the correspondence between the type IIB supergravity in the pp-wave background and its dual supersymmetric Yang-Mills theory at the interaction level. We first construct the cubic term of the light-cone interaction Hamiltonian for the dilaton-axion sector of the supergravity. Our result agrees with the corresponding part of the light-cone string field theory (SFT) and furthermore fixes its previously undetermined $p^+$-dependent normalization. Adopting thus fixed light-cone SFT, we compute the matrix elements of light-cone Hamiltonian involving three chiral primary states and find an agreement with a prediction from the dual Yang-Mills theory.