Cubic Interactions in PP-Wave Light Cone String Field Theory

TL;DR

This paper clarifies the role of the cubic interaction prefactor in pp-wave light-cone string field theory and tests the BMN correspondence by comparing $H_3$ matrix elements to ${\cal N}=4$ SYM three-point functions. It shows that for purely bosonic, on-shell (supergravity) modes the prefactor factors to yield the expected dressing $\mu(\Delta_3-\Delta_1-\Delta_2)$ and that the resulting overlaps reproduce $C_{123}$ in the large $N$ limit, reinforcing the gauge/string duality in this setting. Conversely, all on-shell cubic interactions vanish for these energy-preserving processes, both for bosonic and fermionic sectors, highlighting constraints on dynamical couplings in pp-wave SFT. The work also discusses subtleties with Neumann coefficients and outlines future work to extend beyond the supergravity sector.

Abstract

We use the supergravity modes to clarify the role of the prefactor in the light-cone superstring field theory on PP-wave background. We verify some of the proposals of the recent paper hep-th/0205089 and give further evidence for the correspondence between N=4 SYM gauge theory and string theory on PP-wave. We also consider energy-preserving processes and find that they give vanishing cubic interaction Hamiltonian matrix.