Tracing the String: BMN correspondence at Finite J^2/N

TL;DR

This paper establishes a detailed correspondence between BMN operators in N=4 gauge theory and string states in dual string field theory at finite coupling, confirming predictions about mass shifts and interaction amplitudes.

Contribution

It identifies a basis transformation linking gauge theory operators to string states at finite g_2, and predicts contact terms and mass renormalization consistent with gauge theory results.

Findings

Matching of 3-string amplitudes with gauge theory calculations

Prediction of order g_2^2 contact terms in the string Hamiltonian

Agreement of string state mass shifts with conformal dimension changes

Abstract

Employing the string bit formalism of hep-th/0209215, we identify the basis transformation that relates BMN operators in N=4 gauge theory to string states in the dual string field theory at finite g_2=J^2/N. In this basis, the supercharge truncates at linear order in g_2, and the mixing amplitude between 1 and 2-string states precisely matches with the (corrected) answer of hep-th/0206073 for the 3-string amplitude in light-cone string field theory. Supersymmetry then predicts the order g_2^2 contact term in the string bit Hamiltonian. The resulting leading order mass renormalization of string states agrees with the recently computed shift in conformal dimension of BMN operators in the gauge theory.