Borel summability of a four-dimensional field theory

Abstract

Borel summability of any renormalizable euclidean field theory which is planar, asymptotically free, massive, and whose coupling constant is sufficiently small can be proven. The simplest example is massive Tr 4 in the N ¨ limit, with the 'wrong' sign of . An outline of the proof is given. Our methods also yield further information on the analyticity of the Borel function for massless theories.