Constraining integrable AdS/CFT with factorized scattering

Understand

We consider (warped) AdS string backgrounds which allow for a GKP spinning string/null cusp solution.

• Integrability implies that the worldsheet S-matrix should factorize, which in turn constrains the form of the warp factor as a function of the coordinates of the internal space.
• This constraint is argued to rule out integrability for all supersymmetric AdS7 and AdS6 backgrounds as well as AdS5 Gaiotto-Maldacena backgrounds and a few highly supersymmetric AdS4 and AdS3 backgrounds.