Three-parameter deformation of ℝ × S 3 in the Landau-Lifshitz limit

Abstract In this article we construct the effective field theory associated to the ℝ × S 3 sector of the three-parameter deformation of AdS3 × S 3 × T 4 in the Landau-Lifshitz approximation. We use this action to compute the dispersion relation of excitations around the BMN vacuum and the perturbative S-matrix associated to them. We are able to compute and sum all the different loop contributions to the S-matrix in this limit