Instantons or Renormalons? A Comment on phi4_4 Theory in the MS Scheme

TL;DR

Recent high-order calculations in four-dimensional phi^4 theory suggest instantons, not renormalons, dominate large order behavior, supporting the idea that MS scheme functions are insensitive to renormalons.

Contribution

This comment highlights the potential dominance of instantons over renormalons in high-order perturbative behavior within the MS scheme.

Findings

Six- and seven-loop computations indicate instanton dominance.

Results support the conjecture that MS scheme functions are insensitive to renormalons.

Large order behavior aligns with instanton-based predictions.

Abstract

We comment that the recent exact six-loop and seven-loop computations of renormalization group functions for the O(N)-symmetric four dimensional phi^4 quantum field theory show hints that the associated large order behavior is dominated by instantons rather than renormalons. This is consistent with a long-standing conjecture that renormalization group functions in the minimal subtraction (MS) renormalization scheme are not sensitive to renormalons.