  We derive the perturbative four loop anomalous dimension of the Konishi
operator in N=4 SYM theory from the integrable string sigma model by evaluating
the finite size effects using Luscher formulas adapted to multimagnon states at
weak coupling. We obtain these multiparticle generalizations of Luscher
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.
