“Chiral” field theory, fishnets and integrable spin chains

In this talk I will review the work that has been done by me, N. Gromov, V. Kazakov, G. Korchemsky and G. Sizov on the analysis of fishnet Feynman graphs in a particular scaling limit of $\mathcal N=4$ SYM, a theory dubbed $\chi$FT$_4$. After introducing said theory, in which the Feynman graphs take a very simple fishnet form — in the planar limit — I will review how to exploit integrable techniques to compute these graphs and, consequently, extract the anomalous dimensions of a simple class of operators.