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Schur-Weyl duality and large $N$ limit in 2d Yang-Mills theory

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Wilson loops are the basic observables of Yang-Mills theory, and their expectation is rigorously defined on the Euclidean plane and on a compact Riemannian surface. Focusing on the case where the structure group is the unitary group $U(N)$, I will present a formula that computes any Wilson loop expectation in almost purely combinatorial terms, thanks to the dictionary between unitary and symmetric quantities provided by the Schur-Weyl duality. This formula should be applicable to the computation of the large $N$ limit of the Wilson loop expectations, also called the master field, and of which the existence on the sphere was proved by Antoine Dahlqvist and James Norris.

This talk is part of the Probability series.

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