Ambiguities of renormalized φ 44 field theory and the singularities of its borel transform

Abstract

The analytic structure of the Borel transform of renormalized φ 4 4 theory can be deduced from the small regulator expansion of the regularized theory. The coefficients of Symanzik's local effective lagrangian describing this expansion are shown to be ambiguous, although well defined in perturbation. We deduce that the UV singularities of the Borel transform (renormalons) of φ 4 4 are proportional to insertions of local composite operators, as conjectured by Parisi. However, the renormalization group functions do not a priori contain renormalons. This can be proven at all orders of the 1 N expansion.