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CATEGORIES:Probability
SUMMARY:Wilson loop expectations as sums over surfaces in
2D - Minjae Park (MIT)
DTSTART;TZID=Europe/London:20210615T160000
DTEND;TZID=Europe/London:20210615T170000
UID:TALK160903AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/160903
DESCRIPTION:Although lattice Yang-Mills theory on ℤᵈ is easy t
o rigorously define\, the construction of a satisf
actory continuum theory on ℝᵈ is a major open prob
lem when d ≥ 3. Such a theory should assign a Wils
on loop expectation to each suitable collection ℒ
of loops in ℝᵈ. One classical approach is to try t
o represent this expectation as a sum over surface
s with boundary ℒ. There are some formal/heuristic
ways to make sense of this notion\, but they typi
cally yield an ill-defined difference of infinitie
s.\n\nIn this talk\, we show how to make sense of
Yang-Mills integrals as surface sums for d=2\, whe
re the continuum theory is already understood. We
also obtain an alternative proof of the Makeenko-M
igdal equation and generalized Lévy's formula.\n\n
Joint work with Joshua Pfeffer\, Scott Sheffield\,
and Pu Yu.
LOCATION:Zoom
CONTACT:Jason Miller
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