Abstract

We compute the large $N$ limit of several objects related to the two-dimensional Euclidean Yang–Mills measure on closed, connected, orientable surfaces $\mathrm{\Sigma }$ with genus $g\ge 1$, when a structure group is taken among the classical groups of order $N$. We first generalise to all classical groups the convergence of partitions functions obtained by the second author for unitary groups. We then apply this result to prove convergence of Wilson loop observables for loops included within a topological disc of $\mathrm{\Sigma }$. This convergence solves a conjecture of B. Hall and shows moreover that the limit is independent of the topology of $\mathrm{\Sigma }$ and is equal to an evaluation of the planar master field. Using similar arguments, we show that Wilson loops vanish asymptotically for all noncontractible simple loops.

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