Tracing the string: BMN correspondence at finite J²/N

Employing the string bit formalism of [18], 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 g₂ = J²/N. In this basis, the supercharge truncates at linear order in g2, and the mixing amplitude between 1 and 2-string states precisely matches with the (corrected) answer of [5] for the 3-string amplitude in light-cone string field theory. Supersymmetry then predicts the order g₂² 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.