## Wilson loop expectations as sums over surfaces in 2D

### With Minjae Park (MIT)

# Wilson loop expectations as sums over surfaces in 2D

Although lattice Yang-Mills theory on ℤᵈ is easy to rigorously define, the construction of a satisfactory continuum theory on ℝᵈ is a major open problem when d ≥ 3. Such a theory should assign a Wilson loop expectation to each suitable collection ℒ of loops in ℝᵈ. One classical approach is to try to represent this expectation as a sum over surfaces with boundary ℒ. There are some formal/heuristic ways to make sense of this notion, but they typically yield an ill-defined difference of infinities.

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 generalized Lévy’s formula.

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

- Speaker: Minjae Park (MIT)
- Tuesday 15 June 2021, 16:00–17:00
- Venue: Zoom.
- Series: Probability; organiser: Jason Miller.