Conformal Fishnet Theory

I will give an overview of recent study of a family of four-dimensional  non-supersymmetric and non-unitary CFTs emerging as a special double scaling limit of deformed N=4 SYM theory.  A particular, single coupling case of these models is dominated by "fishnet" planar Feynman graphs having a shape of regular square lattice. This CFT can be generalized to any dimension. Planar Feynman graphs  of the general, 3-coupling  model of this type  still have a kind of dynamical fishnet structure.  The fishnet CFT inherits the integrability of planar N=4 SYM. It appears to be directly related to the integrability of conformal 1+1-dimensional Heisenberg spin chain.


I present the results of explicit all-loop computations of certain four-point correlation functions  and of the related OPE data.