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Explore an advanced physics lecture examining the Checkerboard conformal field theory (CFT) and its role within non-unitary, logarithmic Fishnet CFTs. Delve into the mathematical structure of planar Feynman graphs arranged in regular square lattices with checkerboard coloring, where each colored cell represents an R-matrix in principal series representations of the conformal group. Learn about perturbative and numerical computations of anomalous dimensions in two key reductions: the Fishnet limit of twisted ABJM theory in 3D and a 2D reduction containing BFKL Pomeron energy. Examine analytical expressions for Checkerboard analogues of Basso-Dixon 4-point functions and Diamond-type 4-point graphs with disc topology, while understanding their properties through operator product expansion (OPE) for operators with open indices. Discover how quantum corrections in the spectrum occur at even orders in loop expansion and explore a conjectured modification with periodic loop order corrections, presented by Associate Professor Mikhail Alfimov, an expert in integrable quantum field theories from HSE University and Moscow Engineering-Physical Institute.
