Speaker: Moritz Kade (HU Berlin)

Title: Integrable systems: From the ice rule to supersymmetric fishnet Feynman diagrams

Abstract:
This defense presents the correspondence between models of statistical physics and Feynman graphs of quantum field theories by a common property: integrability. I review integrable structures on both sides, while focusing on the six-vertex model and the superfishnet theory. The latter is a double-scaled beta-deformation of N = 4 super Yang-Mills theory. I present new box-shaped boundary conditions for the six-vertex model and conjecture a closed form for its partition function at any lattice size. On the QFT side, we find integrable boundary scattering matrices in the form of generalized Feynman diagrams by graphical methods. By establishing an efficient, similar graphical formalism, we obtain the critical coupling of the superfishnet theory. Moreover, we apply superspace methods to the superfishnet theory and find results for anomalous dimensions and an OPE coefficient, which are all-loop exact in the coupling.