Four-loop perturbative Konishi from strings and finite size effects for multiparticle states

We derive the perturbative four loop anomalous dimension of the Konishi operator in N=4N=4 SYM theory from the integrable string sigma model by evaluating the finite size effects using Lüscher formulas adapted to multimagnon states at weak coupling. We obtain these multiparticle generalizations of Lüscher formulas by studying certain exactly solvable relativistic integrable quantum field theories. The final result involves a summation of all bound states in the mirror theory and agrees with gauge theory perturbative computations.