Confinement as Analytic Continuation Beyond Infinity

Abstract

We propose a mechanism for confinement: analytic continuation beyond infinite coupling in the space of the coupling constant. The analytic continuation is realized by renormalization group flows from the weak to the strong coupling regime. We demonstrate this mechanism explicitly for the mass gap in two-dimensional sigma models in the large $N$ limit. Our analysis suggests that the conventional analysis of the operator product expansion in itself does not necessarily guarantee the existence of a classical solution corresponding to renormalons. We discuss how the renormalon puzzle may be resolved by the analytic continuation beyond infinite coupling.

5 pages; v2: published version

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Cited by in corpus (5)

• Resurgence and renormalons in the one-dimensional Hubbard model
• Lattice $\mathbb{C}{P}^{N-1}$ model with ${\mathbb{Z}}_N$ twisted boundary condition: bions, adiabatic continuity and pseudo-entropy
• A new renormalon in two dimensions
• Self-Dualities and Renormalization Dependence of the Phase Diagram in 3d $O(N)$ Vector Models
• Identification of perturbative ambiguity canceled against bion