PP-wave String Interactions from String Bit Model

TL;DR

This work tests the BMN correspondence by constructing explicit single- and multi-string states within a quantum-mechanical orbifold (string-bit) model and computing their three-point functions and light-cone Hamiltonian matrix elements to order $g_2^2$. The authors derive these observables from first principles using the $\Sigma$ operator that governs string joining/splitting, obtaining closed-form expressions that reduce to known perturbative ${\cal N}=4$ SYM results in the BMN limit. The key contribution is demonstrating exact agreement with gauge theory up to $g_2^2$ without assuming free SYM three-point functions, thereby providing a nontrivial consistency check of the interacting string-bit framework on pp-wave backgrounds. This strengthens the bridge between string interactions in the pp-wave setting and the dual gauge theory, and points to further avenues such as alternative oscillator realizations and extensions to more general twisted sectors.

Abstract

We construct the string states $|O_{p}^J>_J$, $|O_{q}^{J_1}>_{{J_1}{J_2}}$ and $|O_{0}^{J_{1}J_{2}}>_{{J_1}{J_2}}$ in the Hilbert space of the quantum mechanical orbifold model so as to calculate the three point functions and the matrix elements of the light-cone Hamiltonian from the interacting string bit model. With these string states we show that the three point functions and the matrix elements of the Hamiltonian derived from the interacting string bit model up to $g^{2}_2$ order precisely match with those computed from the perturbative SYM theory in BMN limit.