Worldsheet scattering for the GKP string

We initiate the perturbative study of the S-matrix for the excitations on top of the GKP vacuum at strong coupling. Using the string sigma model action expanded around the null cusp classical solution, we compute the tree-level S-matrix elements and compare them with the predictions from the asymptotic Bethe Ansatz. We also check the factorization of the three-body S-matrix for various bosonic processes, finding precise agreement with the constraints imposed by integrability.