High orders of perturbation theory: are renormalons significant?

According to Lipatov, the high orders of perturbation theory are determinedby saddle-point configurations (instantons) of the corresponding functionalintegrals. According to t'Hooft, some individual large diagrams, renormalons,are also significant and they are not contained in the Lipatov contribution.The history of the conception of renormalons is presented, and the arguments infavor of and against their significance are discussed. The analytic propertiesof the Borel transforms of functional integrals, Green functions, vertex parts,and scaling functions are investigated in the case of \phi^4 theory. Theiranalyticity in a complex plane with a cut from the first instanton singularityto infinity (the Le Guillou - Zinn-Justin hypothesis) is proved. It rules outthe existence of the renormalon singularities pointed out by t'Hooft anddemonstrates the nonconstructiveness of the conception of renormalons as awhole. The results can be interpreted as an indication of the internalconsistency of \phi^4 theory