Conformal Fishnet Theory in any dimension

by Vladimir Kazakov (Laboratoire de Physique Theorique)

Thursday 23 May 2019, 14:00 → 16:00 Europe/Zurich

4/3-006 - TH Conference Room (CERN)

Fishnet conformal field theory (FCFT) in 4D was proposed in 2015 by O.Gurdogan and myself as a specific, double scaling limit of the maximally supersymmetric, gamma-deformed super Yang-Mills theory. The FCFT inherits the planar integrability of N=4 SYM but has a much simpler planar graph content and no supersymmetry. The simplest version of FCFT contains only two interacting complex scalar fields, and its typical Feynman graphs are of the regular square lattice shape. The latter has been introduced by A.Zamolodchikov  in 1980 as an example of solvable statistical-mechanical model of non-compact spins on 4D conformal group. The FCFT appears to be a remarkable tool for computations of non-trivial Feynman graphs of that type.  This integrable FCFT can be generalized to any dimension D.  I will briefly present the basics of FCFT integrability and review recent exact all-loop results for various physical quantities: 4-point correlators, anomalous dimensions of "wheel" and "spiral" operators, scalar amplitudes, etc. The FCFT  has some exotic features: it is a non-unitarity, logarithmic CFT. Nevertheless, it presents a unique opportunity for insights into non-perturbative, non-supersymmetric conformal physics in any dimension.