Wilson loop expectations as sums over surfaces in 2D

Add to your list(s) Download to your calendar using vCal

• Minjae Park (MIT)
• Tuesday 15 June 2021, 16:00-17:00
• Zoom.

If you have a question about this talk, please contact Jason Miller.

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.

This talk is part of the Probability series.

This talk is included in these lists:

• All CMS events
• All Talks (aka the CURE list)
• CMS Events
• DPMMS Lists
• DPMMS info aggregator
• DPMMS lists
• Hanchen DaDaDash
• Interested Talks
• Probability
• School of Physical Sciences
• Statistical Laboratory info aggregator
• Zoom
• bld31

Note that ex-directory lists are not shown.