High Energy Theory Seminar

I will review the proprieties and recent results for conformal fishnet theory (FCFT) which was proposed by O.Gurdogan and myself as a special double scaling limit of gamma-deformed N=4 SYM theory.  FCFT, in its simplest, bi-scalar version, is a UV finite strongly coupled 4-dimensionl logarithmic CFT dominated by planar fishnet Feynman graphs (of the shape of regular square lattice). FCFT inherits the planar integrability of N=4 SYM which becomes manifest  in this case:  the  fishnet graphs  can be mapped on the SO(2,4) integrable spin chain (A.Zamolodchikov 1980). The D-dimensional generalization of FCFT, with SO(2,D) conformal symmetry can be also provided.  A remarkable property of FCFT is the possibility of spontaneous symmetry breaking,  due to the flat vacua which are not lifted by quantum corrections. I will also discuss the exact computation of certain anomalous dimensions and   4-point correlators, and of related fishnet Feynman graphs (of "wheel" or "spiral" type), using the quantum integrability tools: asymptotic and thermodynamic Bethe ansatz and quantum spectral curve of N=4 SYM.