Abstract
We give three short proofs of the Makeenko–Migdal equation for the Yang–Mills measure on the plane, two using the edge variables and one using the loop or lasso variables. Our proofs are significantly simpler than the earlier pioneering rigorous proofs given by Lévy and by Dahlqvist. In particular, our proofs are “local” in nature, in that they involve only derivatives with respect to variables adjacent to the crossing in question. In an accompanying paper with Gabriel, we show that two of our proofs can be adapted to the case of Yang–Mills theory on any compact surface.
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Communicated by S. Zelditch
B.C. Hall was supported in part by NSF Grant DMS-1301534. T. Kemp was supported in part by NSF CAREER Award DMS-1254807.
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Driver, B.K., Hall, B.C. & Kemp, T. Three Proofs of the Makeenko–Migdal Equation for Yang–Mills Theory on the Plane. Commun. Math. Phys. 351, 741–774 (2017). https://doi.org/10.1007/s00220-016-2793-6
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DOI: https://doi.org/10.1007/s00220-016-2793-6