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SUMMARY:Wilson loop expectations as sums over surfaces in 2D - Minjae Park
  (MIT)
DTSTART:20210615T150000Z
DTEND:20210615T160000Z
UID:TALK160903@talks.cam.ac.uk
CONTACT:Jason Miller
DESCRIPTION:Although lattice Yang-Mills theory on ℤᵈ is easy to rigoro
 usly 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 Wi
 lson loop expectation to each suitable collection ℒ of loops in ℝᵈ. 
 One classical approach is to try to represent this expectation as a sum ov
 er surfaces with boundary ℒ. There are some formal/heuristic ways to mak
 e sense of this notion\, but they typically yield an ill-defined differenc
 e of infinities.\n\nIn 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 eq
 uation and generalized Lévy's formula.\n\nJoint work with Joshua Pfeffer\
 , Scott Sheffield\, and Pu Yu.
LOCATION:Zoom
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