Large N limit of Yang-Mills partition function and Wilson loops on compact surfaces

Abstract

We compute the large N limit of several objects related to the two-dimensional Euclidean Yang-Mills measure on compact connected orientable surfaces Σ of genus g ≥ 1 with a structure group 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 in [29], then we apply this result to show that all Wilson loop observables for loops included within a topological disc of Σ converge towards the limit of the Wilson loop where the latter disc is embedded in the plane in place of Σ. This solves a conjecture of B. Hall [25] for closed surfaces. Besides, using similar arguments, we show that Wilson loops vanish for all non-contractible simple loops.