Makeenko-Migdal Equations for 2D Yang-Mills: From Lattice to Continuum

This lecture explores Wilson loops as key observables in the Yang-Mills model, focusing on the Makeenko-Migdal equations (also known as loop equations). Discover how these equations, which function as integration by parts or Dyson-Schwinger equations in Yang-Mills theory, have been rigorously established both on lattices of various dimensions (through work by Chatterjee, Cao-Park-Sheffield, and others) and in 2D continuum (by researchers including Levy, Dahlqvist, and Driver-Hall-Kemp). Learn about the speaker's research demonstrating that in two dimensions, lattice Makeenko-Migdal equations converge to their continuum counterparts under appropriate conditions. The presentation covers joint work with S. Smith and R. Zhu, providing mathematical insights into this important connection between discrete and continuous formulations in quantum field theory.