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Wilson loop expectations as sums over surfaces in 2D

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If you have a question about this talk, please contact Perla Sousi .

Although lattice Yang-Mills theory on β„€α΅ˆ is easy to rigorously define, the construction of a satisfactory continuum theory on β„α΅ˆ is a major open problem when d β‰₯ 3. Such a theory should assign a Wilson loop expectation to each suitable collection β„’ of loops in β„α΅ˆ. One classical approach is to try to represent this expectation as a sum over surfaces with boundary β„’. 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 LΓ©vy’s formula.

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

This talk is part of the Probability series.

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