The lattice formulation of quantum Yang-Mills theory allows for all quantities to be computed in terms of well-defined random matrix integrals. In this talk, we consider the case of dimension two, for which a continuum limit (due to Migdal-Witten) is known and exactly solvable. We discuss two mysterious occurrences of stochastic analysis in this setting: (1) the appearance of GUE integrals arising from heat kernel asymptotics and complex-analytic integrals; (2) an adaptation of stochastic calculus to "Gaussian" free fields that have indefinite covariance matrix. These results fall under the author's program of investigating the relationship between lattice and continuum quantum gauge theories.
Speaker(s): Timothy Nguyen (Michigan State University)