A semiclassical realization of infrared renormalons

TL;DR

This paper proposes a semiclassical framework on R**3 x S**1 to realize infrared renormalons in quantum field theory, linking Borel plane singularities to specific saddle point configurations like bion--anti-bion events.

Contribution

It extends semiclassical analysis to identify saddle point configurations corresponding to IR renormalons in gauge theories, providing a new understanding of their origin.

Findings

Identifies saddle point configurations related to IR renormalons.

Shows these configurations are closer to the origin in the Borel plane by a factor of N.

Proposes these configurations as the semiclassical realization of renormalons.

Abstract

Perturbation series in quantum field theory are generally divergent asymptotic series which are also typically not Borel resummable in the sense that the resummed series is ambiguous. The ambiguity is associated with singularities in the Borel plane on the positive real axis. In quantum mechanics there are cases in which the ambiguity that arises in perturbation theory cancels against a similarly ambiguous contribution from instanton--anti-instanton events. In asymptotically free gauge theories this mechanism does not suffice because perturbation theory develops ambiguities associated with singularities in the Borel plane which are closer to the origin by a factor of about N (the rank of the gauge group) compared to the singularities realized by instanton events. These are called IR renormalon poles, and on R**4 they do not possess any known semiclassical realization. By using continuity on R**3 x S**1, and by generalizing the works of Bogomolny and Zinn-Justin to QFT, we identify saddle point field configurations, e.g., bion--anti-bion events, corresponding to singularities in the Borel plane which are of order N times closer to the origin than the 4d BPST instanton--anti-instanton singularity. We conjecture that these are the leading singularities in the Borel plane and that they are the incarnation of the elusive renormalons in the weak coupling regime.