Particle production in a light-cone gauge fixed Jordanian deformation of $Ad{S}_5\times S^5$

We consider a string on a Jordanian deformation of the $Ad{S}_5\times S^5$ spacetime. This model belongs to the larger class of Homogeneous Yang-Baxter deformations, which preserve classical integrability in the sense that one can construct an explicit Lax connection. To study the scattering of bosonic worldsheet excitations, we fix light-cone gauge and expand around a pointlike classical solution that reduces to the BMN vacuum in the undeformed limit. Our analysis shows that the light-cone gauge-fixed Hamiltonian, under a perturbative field expansion, includes cubic terms that give rise to non-trivial cubic processes for physical particles. We discuss this unexpected result in relation to the property of Lax integrability of the sigma-model.