Local Fields in Lattice Models and Conformal Field Theories

Explore the mathematical connection between probabilistic lattice models and conformal field theories through this 59-minute lecture from the Hausdorff Center for Mathematics. Discover how physicists in the 1980s conjectured that scaling limits of critical lattice models should correspond to conformal field theories, where the state space consists of local fields and observables are their correlation functions. Learn how discrete complex analysis enables the construction of lattice model local fields with Virasoro algebra representations, creating structured correspondences between CFT and lattice discretization spaces. Examine the proof that local fields of the discrete Gaussian Free Field gradient form a Fock space isomorphic to free bosonic CFT, with properly renormalized correlations converging to CFT correlation functions in the scaling limit according to Virasoro generator eigenvalues. Understand the ongoing research progress toward achieving similar complete CFT descriptions for the Ising model, based on collaborative work with researchers from EPFL Lausanne, KTH Stockholm, University of Michigan, and University of Helsinki.