IR Renormalons vs. Operator Product Expansion in Supersymmetric and Related Gauge Theories

TL;DR

This paper investigates the relationship between IR renormalons and condensates in supersymmetric and related gauge theories, predicting singularity structures in the Borel plane and clarifying the role of instantons and the limitations of bubble-chain methods.

Contribution

It demonstrates the 'conspiracy' between IR renormalons and condensates across different gauge theories, providing new insights into their singularity structures and the validity of instanton contributions.

Findings

IR renormalons and condensates are linked in supersymmetric theories.

Absence of renormalons implies well-defined instanton contributions.

Bubble-chain method is insufficient for detecting renormalon divergences.

Abstract

We use the "conspiracy" between infrared (IR) renormalons and condensates in the operator product expansion for correlation functions to make predictions concerning the structure of singularities in the Borel plane for the perturbative series in quantum field theories with different levels of supersymmetry. The same conspiracy can be used for establishing the absence of condensates or IR renormalons in gauge theories with an IR conformal regime or fully Higgsed gauge theories. The absence of the renormalon-induced factorial divergence implies that instanton contributions (where present) must be well-defined. We show that the conventional bubble-chain method for detecting renormalon-induced factorial divergences in these theories is not sufficient.