  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 backgrounds by analysing tree-level
scattering of two AdS bosons into two fermions on the worldsheet of a BMN
string. We find a condition which can be efficiently used to rule out
integrability of AdS strings and therefore of the corresponding AdS/CFT
dualities, as we demonstrate for some simple examples.
