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

References in corpus (1)

• Mastering the Master Field

Cited by in corpus (14)

• A Perspective on Constructive Quantum Field Theory
• Three proofs of the Makeenko-Migdal equation for Yang-Mills theory on the plane
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• Free energies and fluctuations for the Unitary Brownian Motion
• Random Unitary Representations of Surface Groups I: Asymptotic expansions
• Large $N$ limit of the $O(N)$ linear sigma model in 3D
• The generalized master fields
• The large-N limit for two-dimensional Yang-Mills theory
• Large N limit of Yang-Mills partition function and Wilson loops on compact surfaces
• 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