|DATE||December 21 (Tue), 2021|
|TITLE||Wilson loop expectations as sums over surfaces in 2D Yang-Mills theory|
|ABSTRACT||Although lattice Yang-Mills theory on ?? is easy to rigorously define, the construction of a satisfactory continuum theory on ?? is a major open problem when d ≥ 3. Such a theory should assign a Wilson loop expectation to each suitable collection ? of loops in ??. One classical approach is to try to represent this expectation as a sum over surfaces with boundary ?. There are some formal/heuristic ways to make sense of this notion, but they typically yield an ill-defined difference of infinities.
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In this talk, we show how to make sense of Yang-Mills integrals as surface sums for d=2, where the continuum theory is already understood. We also obtain an alternative proof of the Makeenko-Migdal equation and a version of the Gross-Taylor expansion. Joint work with Joshua Pfeffer, Scott Sheffield, and Pu Yu.