Infrared Renormalons versus Operator Product Expansions in Supersymmetric and Related Gauge Theories

We use the connection 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 gauge theories in the Higgs phase. 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.

Figure 1

The bubble-chain diagram for a two-point function associated with renormalons. Solid lines denote quark propagators, while dashed lines are for gluons.

Figure 2

Anomalous dimensions of the matter fields in SQCD.

Figure 3

In asymptotically free IR-conformal field theories, for example, in the Banks-Zaks limit [19], the coupling constant runs at high energies, but reaches a fixed point ${\alpha }_{*}$ at low energies.