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

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.

arXiv comment12 pages; 7 figures; v2: typos corrected, published version in PRD

References in corpus (16)

• The anomalous magnetic moment of the muon in the Standard Model
• Perturbative Quantum Gravity as a Double Copy of Gauge Theory
• Renormalons
• The Amplituhedron
• Tenth-Order QED Contribution to the Electron g-2 and an Improved Value of the Fine Structure Constant
• The five-loop beta function of Yang-Mills theory with fermions
• Minimally subtracted six loop renormalization of $O(n)$-symmetric ${\varphi }^4$ theory and critical exponents
• Numbers and Functions in Quantum Field Theory
• Knots and Numbers in ${\varphi }^4$ Theory to 7 Loops and Beyond
• Five-loop renormalization group functions of $O(n)$-symmetric ${\varphi }^4$-theory and $\ep$-expansions of critical exponents up to $\ep^5$
• Pade Approximants, Borel Transforms and Renormalons: the Bjorken Sum Rule as a Case Study
• The Galois coaction on ${\varphi }^4$ periods
• Analytical five-loop expressions for the renormalization group QED $\beta$-function in different renormalization schemes
• Perturbation expansions at large order: Results for scalar field theories revisited
• Renormalization Scheme Dependence, RG Flow and Borel Summability in ${\varphi }^4$ Theories in $d<4$
• Self-Dualities and Renormalization Dependence of the Phase Diagram in 3d $O(N)$ Vector Models

Cited by in corpus (8)

• Tropical Feynman integration in the Minkowski regime
• Resonant resurgent asymptotics from quantum field theory
• Recursive computation of Feynman periods
• The analytic structure of the fixed charge expansion
• Resurgence and self-completion in renormalized gauge theories
• Search for an Ultraviolet Zero in the Seven-Loop Beta Function of the $\lambda {\varphi }_4^4$ Theory
• Feynman integrals at large loop order and the $\log$-$\Gamma$ distribution
• Tropicalized quantum field theory and global tropical sampling