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Title: Semiclassical origin of renormalons in asymptotically free theories
Plain: The factorial growth of perturbation series in QCD-like theories is linked to singularities called renormalons, which no known classical solution explains. What nonperturbative object cancels their ambiguity is unknown.
Precise: In asymptotically free theories (4D Yang-Mills and QCD, 2D $O(N)$, $CP^{N-1}$ and principal chiral models), the Borel transform of perturbation series has renormalon singularities at positions set by the one-loop beta-function coefficient, not matched by any finite-action classical solution. Identify the nonperturbative sectors (saddles, fractional instantons, bions on R^{d-1} x S^1, or OPE condensates) whose imaginary ambiguities cancel the renormalon ambiguities, and demonstrate the cancellation.
Settled by: An explicit computation in at least one asymptotically free theory showing order-by-order cancellation between the renormalon ambiguity and an identified nonperturbative sector.
Kind: phenomenon
Answer type: mechanism
References: (empty)
Literature status: contested
Status note: Bion proposals (2012) were questioned when their ambiguities did not match renormalon positions in compactified $\mathrm{CP}^{N-1}$ and $\mathrm{O}(N)$ models (2019-2024).
Posed since: (empty)