Three proofs of the Makeenko-Migdal equation for Yang-Mills theory on the plane

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 T. Lévy and by A. 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 F. Gabriel, we will show that two of our proofs can be adapted to the case of Yang-Mills theory on a compact surface.

Final version. One of the three proofs was rewritten for greater clarity. To appear in Communications in Mathematical Physics

References in corpus (1)

• Three proofs of the Makeenko-Migdal equation for Yang-Mills theory on the plane

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