Confinement as Analytic Continuation Beyond Infinity

TL;DR

This paper introduces a novel confinement mechanism via analytic continuation beyond infinite coupling, demonstrated in 2D sigma models, challenging traditional views on operator product expansion and renormalons.

Contribution

It proposes a new confinement mechanism based on analytic continuation beyond infinite coupling, with explicit demonstration in large N 2D sigma models.

Findings

Confinement can be achieved through analytic continuation beyond infinite coupling.

The analysis questions the sufficiency of operator product expansion for classical solutions.

Renormalon issues may be resolved by this analytic continuation approach.

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.