The borel transform in Euclidean ? v 4 local existence for Rev < 4

Abstract

We consider the ϕ4 theory in Euclidean space of complex dimensionv and prove that, for Rev < 4 the renormalized Feynman amplitudes grow at worst exponentially in the number of vertices in the graph. This implies that the Borel transform of any Schwinger function may be defined in a neighborhood of the origin in the Borel plane.