How Accurate is Perturbation Theory? A Look at 2D Quantum Yang-Mills

A tacit assumption in quantum field theory is that perturbative expansions in terms of Feynman diagrams approximate in some way the full theory. While this has been confirmed by experiment in important cases, from a mathematical point of view, this belief is unsatisfactory since the full theory often does not exist to begin with. On the other hand, 2D Yang-Mills is an interesting theory that does have a rigorous QFT construction via, e.g., stochastic methods. In this talk, we discuss the rigorous construction of 2D Yang-Mills and compare it with perturbative computations of Wilson loops. We find some (mathematically) unexpected agreement at one loop and expect that an analysis at higher loop order should lead to some further interesting developments.