Finite-size effect for four-loop Konishi of the β-deformed N=4 SYM

We propose that certain twists of the su(2|2) S-matrix elements describe the β-deformation of N=4 supersymmetric Yang-Mills theory. We compute the perturbative four-loop anomalous dimension of the Konishi operator of the deformed gauge theory from the Lüscher formula based on these twisted S-matrix elements. The result agrees exactly with the perturbative gauge theory computations.