Quantum Free Yang-Mills on the Plane

Abstract

We construct a free-probability quantum Yang-Mills theory on the two dimensional plane, determine the Wilson loop expectation values, and show that this theory is the $N=\infty$ limit of U(N) quantum Yang-Mills theory on the plane.

24 pages, tikz figures

Cited by in corpus (14)

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• Large $N$ limit of the $O(N)$ linear sigma model in 3D
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• A combinatorial theory of random matrices III: random walks on $\mathfrak{S}(N)$, ramified coverings and the $\mathfrak{S}(\infty )$ Yang-Mills measure
• A stochastic PDE approach to large N problems in quantum field theory: a survey
• Large $N$ behaviour of the two-dimensional Yang-Mills partition function
• The Segal-Bargmann transform for unitary groups in the large-N limit
• Wilson loop expectations as sums over surfaces on the plane