# MIT Probability Seminar

Monday, May 17, 2021 at 4:15pm to 5:15pm

Virtual Event

Speaker:

Title: Wilson loop expectations as sums over surfaces in 2D

Abstract:  Although lattice Yang-Mills theory on \$ℤ^d\$ is easy to rigorously define, the construction of a satisfactory continuum theory on \$ℝ^d\$ is a major open problem when d≥3. Such a theory should assign a Wilson loop expectation to each collection of loops in \$ℝ^d\$. One of the proposed approaches involves representing this quantity as a sum over surfaces having the loops as their boundary. There are some formal/heuristic ways to make sense of this notion, but they typically yield an ill-defined difference of infinities. The goal of this talk is to make sense of Yang-Mills integrals as surface sums in the special case that d=2, where the existence of a well-defined continuum theory is already well known. We also obtain an alternative proof of the Makeenko-Migdal equation, and Levy's formula based on the Schur-Weyl duality.

Joint work with Joshua Pfeffer, Scott Sheffield, and Pu Yu.

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aldixon@mit.edu