Abstract
We use the methods of [1] to show that the planar part of the renormalized perturbation theory forϕ 44 -euclidean field theory is Borel-summable on the asymptotically free side of the theory. The Borel sum can therefore be taken as a rigorous definition of theN→∞ limit of a massiveN×N matrix model with a +trgϕ 4 interaction, hence with “wrong sign” ofg. Our construction is relevant for a solution of the ultra-violet problem for planar QCD. We also propose a program for studying the structure of the “renormalons” singularities within the planar world.
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Rivasseau, V. Construction and Borel summability of planar 4-dimensional euclidean field theory. Commun.Math. Phys. 95, 445–486 (1984). https://doi.org/10.1007/BF01210833
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DOI: https://doi.org/10.1007/BF01210833