Deformations of image SYM and integrable spin chain models Original Research Article

Beginning with the planar limit of image SYM theory, we study planar diagrams for field theory deformations of image which are marginal at the free field theory level. We show that the requirement of integrability of the full one-loop dilatation operator in the scalar sector, places very strong constraints on the field theory, so that the only soluble models correspond essentially to orbifolds of image SYM. For these, the associated spin chain model gets twisted boundary conditions that depend on the length of the chain, but which are still integrable. We also show that theories with integrable subsectors appear quite generically, and it is possible to engineer integrable subsectors to have some specific symmetry, however these do not generally lead to full integrability. We also try to construct a theory whose spin chain has quantum group symmetry image as a deformation of the image R-symmetry structure of image SYM. We show that it is not possible to obtain a spin chain with that symmetry from deformations of the scalar potential of image SYM.