Resurgence and self-completion in renormalized gauge theories

Abstract

Under certain assumptions and independent of the instantons, we show that the logarithm expansion of dimensional regularization in quantum field theory needs a nonperturbative completion to have a renormalization-group flow valid at all energies. Then, we show that such nonperturbative completion has the analytic properties of the renormalons, which we find with only a marginal reference to diagrammatic calculations. We demonstrate that renormalon corrections necessarily lead to analyzable functions, namely, resurgent transseries. A detailed analysis of the resurgent properties of the renormalons is provided. The self-consistency of the theory requires these nonperturbative contributions to render the running coupling well-defined at any energy, thus with no Landau pole. We illustrate the point within the case of QED. This way, we explicitly realize the correspondence between the nonperturbative Landau pole scale and the renormalons. What is seen as a Landau pole in perturbation theory is cured by the nonperturbative, resurgent contributions.

28 pages, 1 figure, additional clarifications, more references, version to appear in IJMPA

References in corpus (15)

• Dynamic universality class of the QCD critical point
• An Étude in non-linear Dyson--Schwinger Equations
• Recursion and growth estimates in renormalizable quantum field theory
• Conformal mapping of the Borel plane: going beyond perturbative QCD
• Determination of perturbative QCD coupling from ALEPH $\tau$ decay data using pinched Borel-Laplace and Finite Energy Sum Rules
• Non-local Lagrangians from Renormalons and Analyzable Functions
• Borel-Laplace Sum Rules with $\tau$ decay data, using OPE with improved anomalous dimensions
• Instantons or Renormalons? A Comment on phi4_4 Theory in the MS Scheme
• Resurgence of the QCD Adler function
• Renormalons in a scalar self interacting theory: thermal, thermomagnetic and thermoelectric corrections for all values of temperature
• Quantum phase transition and Resurgence: Lessons from 3d $\mathcal{N}=4$ SQED
• Magnetic renormalons in a scalar self interacting $\lambda {\varphi }^4$ theory
• Thermomagnetic renormalons in a scalar self-interacting $\lambda {\varphi }^4$ theory
• A consistent quantum field theory from dimensional reduction
• Resurgent representation of the Adler function in the large-${\beta }_0$ approximation of QCD

Cited by in corpus (4)

• Minimal Proper-time in Quantum Field Theory
• Quantum Field Theory on Multifractal Spacetime: Varying Dimension and Ultraviolet Completeness
• Gluon Mass Generation from Renormalons and Resurgence
• Uncovering Hidden Patterns: Approximate Resurgent Resummation from Truncated Series