The absence of IR renormalons in gauge theories on ${\mathbb{R}}^3\times {\mathbb{S}}^1$ and what it means for resurgence

Abstract

We analyze the renormalon diagram of gauge theories on ${\mathbb{R}}^3\times {\mathbb{S}}^1$. In particular, we perform exact one loop calculations for the vacuum polarization in QCD with adjoint matter and observe that all infrared logarithms, as functions of the external momentum, cancel between the vacuum part and finite volume part, which eliminates the IR renormalon problem. We argue that the singularities in the Borel plane, arising from the topological neutral bions, are not associated with renormalons, but with the proliferation of the Feynman diagrams. As a byproduct, we obtain, for the first time, an exact one-loop result of the vacuum polarization which can be adapted to the case of thermal compactification of QCD.

arXiv comment35 pages, 3 figures

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Cited by in corpus (7)

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• Fractional instantons and bions in the O(N) model with twisted boundary conditions
• What is QFT? Resurgent trans-series, Lefschetz thimbles, and new exact saddles
• Semiclassical Trans-Series from the Perturbative Hopf-Algebraic Dyson-Schwinger Equations: ${\varphi }^3$ QFT in 6 Dimensions
• On the Global Structure of Deformed Yang-Mills Theory and QCD(adj) on ${\mathbb{R}}^3\times {\mathbb{S}}^1$
• Aspects of Perturbation theory in Quantum Mechanics: The BenderWu Mathematica package
• New nonperturbative scales and glueballs in confining supersymmetric gauge theories