  In this article we construct the effective field theory associated to the
$\mathbb{R}\times S^3$ sector of the three-parameter deformation of $AdS_3
\times S^3 \times T^4$ 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.

High Energy Physics - Theory