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We localize the loop equation of large-N YM theory in the ASD variables on acritical equation for an effective action by means of homological methods asopposed to the cohomological localization of equivariantly closed forms inlocal field theory. Our localization occurs for some special simple quasi BPSWilson loops, that have no perimeter divergence and no cusp anomaly forbacktracking cusps, in a partial Eguchi-Kawai reduction from four to twodimensions of the non-commutative theory in the limit of infinitenon-commutativity and in a lattice regularization in which the ASD integrationvariables live at the points of the lattice, thus implying an embedding ofparabolic Higgs bundles in the YM functional integral. We find that the betafunction of the effective action is saturated by the non-commutative ASDvortices of the EK reduction. An exact canonical beta function of NSVZ typethat reproduces the universal first and second perturbative coefficientsfollows by the localization on vortices. Finally we argue that a scheme can befound in which the canonical coupling coincides with the physical chargebetween static quark sources in the large-N limit and we compare ourtheoretical calculation with some numerical lattice result.

Quasi BPS Wilson loops, localization of loop equation by homology and exact beta function in the large N limit of SU(N) Yang-Mills theory