Semiclassical origin of renormalons in asymptotically free theories · revision history

Revision 2

Accepted · core change · record

Changes against revision 1:

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 · changed · core
Revision 1: 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.
Revision 2: In asymptotically free theories ($4\mathrm{D}$ Yang-Mills and QCD, $2\mathrm{D}$ $\mathrm{O}(N)$, $\mathrm{CP}^{N-1}$ 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)

Decisions