Free BMN Correlators With More Stringy Modes

TL;DR

This paper investigates higher genus free BMN correlators with multiple stringy modes in the pp-wave background, revealing new insights into their positivity properties and holographic relations, especially for four or more string modes.

Contribution

It extends the analysis of BMN correlators to cases with more stringy modes and higher genus, challenging previous positivity assumptions and confirming the holographic factorization formula.

Findings

Non-negativity of torus two-point functions fails for four or more string modes.

The holographic factorization formula remains valid despite positivity issues.

Planar three-point functions match string vertex calculations.

Abstract

In the type IIB maximally supersymmetric pp-wave background, stringy excited modes are described by BMN (Berenstein-Madalcena-Nastase) operators in the dual $\mathcal{N}=4$ super-Yang-Mills theory. In this paper, we continue the studies of higher genus free BMN correlators with more stringy modes, mostly focusing on the case of genus one and four stringy modes in different transverse directions. Surprisingly, we find that the non negativity of torus two-point functions, which is a consequence of a previously proposed probability interpretation and has been verified in the cases with two and three stringy modes, is no longer true for the case of four or more stringy modes. Nevertheless, the factorization formula, which is also a proposed holographic dictionary relating the torus two-point function to a string diagram calculation, is still valid. We also check the correspondence of planar three-point functions with Green-Schwarz string vertex with many string modes. We discuss some issues in the case of multiple stringy modes in the same transverse direction. Our calculations provide some new perspectives on pp-wave holography.