Condition on Ramond-Ramond fluxes for factorization of worldsheet scattering in anti–de Sitter space

Factorization of scattering is the hallmark of integrable $1+1$ dimensional quantum field theories. For factorization of scattering to be possible the set of masses and momenta must be conserved in any two-to-two scattering process. We use this fact to constrain the form of the Ramond-Ramond fluxes for integrable supergravity anti–de Sitter (AdS) backgrounds by analyzing tree-level scattering of two AdS bosons into two fermions on the worldsheet of a Berenstein-Maldacena-Nastase string. We find a condition which can be efficiently used to rule out integrability of AdS strings and therefore of the corresponding AdS/conformal field theory dualities, as we demonstrate for some simple examples.