New QFTs and integrable Feynman graphs from strongly twisted N=4 SYM and ABJM
Vladimir Kazakov (LPTENS, Paris, France)

I discuss the recently proposed by O.Gurdogan and myself new QFTs in 3 and 4 dimensions integrable in planar limit. They emerge in the double scaling limit (strong gamma-deformation, weak coupling) from N=4 SYM and ABJM theories and inherit their integrability. In the simplest case, such a 4D theory reduces simply to two interacting complex scalars with a specific interaction term. Its typical planar graphs are of the "fishnet" type, shown integrable by A.Zamolodchikov (1980) in virtue of the star-triangle relations. For most of the physical quantities (correlators, amplitudes) each order of perturbation theory is defined at most by a single such graph. This allows to use the powerful AdS/CFT integrability tools for computations of new multi-loop Feynman graphs (wheel graphs, spider-web graphs etc.). We will also discuss the relation of these models to non-compact integrable quantum spin chains with the symmetry of 3D and 4D conformal groups.