Constraining integrable AdS/CFT with factorized scattering

Abstract

Abstract 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 AdS 7 and AdS 6 backgrounds as well as AdS 5 Gaiotto-Maldacena backgrounds and a few highly supersymmetric AdS 4 and AdS 3 backgrounds.