Abstract
We show that the Laplace transforms of traces of words in independent unitary Brownian motions converge towards an analytic function on a non trivial disc. These results allow one to study the asymptotic behavior of Wilson loops under the unitary Yang–Mills measure on the plane with a potential. The limiting objects obtained are shown to be characterized by equations analogue to Schwinger–Dyson’s ones, named here after Makeenko and Migdal.
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Dahlqvist, A. Free Energies and Fluctuations for the Unitary Brownian Motion. Commun. Math. Phys. 348, 395–444 (2016). https://doi.org/10.1007/s00220-016-2756-y
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DOI: https://doi.org/10.1007/s00220-016-2756-y