PP-wave string interactions from n-point correlators of BMN operators

TL;DR

This paper provides a concrete realization of the BMN sector of ${\cal N}=4$ SYM by showing that BMN operators close under the OPE in the double scaling limit, enabling a controlled mapping to pp-wave string states. By analyzing short-distance limits of BMN $n$-point correlators, the authors demonstrate a precise correspondence between BMN correlators and tree- and loop-level pp-wave string interactions, with the three-string vertex $C_{IJK}$ and the energy factors $E_K/\mu$ encoding interaction amplitudes and propagators. They extend the dictionary to higher-point functions through systematic pinchings, including a hierarchical scheme for multi-string processes, and discuss loop corrections and the role of cluster decomposition. The instanton analysis suggests no instanton corrections to two-point BMN functions, consistent with the absence of D-instantons in pp-wave backgrounds, while higher-point correlators require case-by-case checks. Overall, the work offers a detailed framework connecting nontrivial multi-point BMN correlators in SYM to pp-wave string interactions, advancing our understanding of the pp-wave/SYM correspondence.

Abstract

BMN operators are characterized by the fact that they have infinite R-charge and finite anomalous dimension in the BMN double scaling limit. Using this fact, we show that the BMN operators close under operator product expansion and form a sector in the N=4 supersymmetric Yang-Mills theory. We then identify short-distance limits of general BMN n-point correlators, and show how they correspond to the pp-wave string interactions. We also discuss instantons in the light of the pp-wave/SYM correspondence.

Figures (4)

• Figure 1: Short OPE of BMN operators and its string interpretation.
• Figure 2: A four-string interaction.
• Figure 3:
• Figure 4: A one-loop corrected string interaction.