In the 2D large-N O(N) quartic model, the large-momentum OPE of the scalar two-point function is divergent: coefficient functions and operator condensates carry n! factorial growths that cancel only off-diagonally, never within a fixed power.
IR Renormalons vs. Operator Product Expansion in Supersymmetric and Related Gauge Theories
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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.
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Renormalon-like factorial enhancements to power expansion/OPE in a super-renormalizable 2D $O(N)$ quartic model
In the 2D large-N O(N) quartic model, the large-momentum OPE of the scalar two-point function is divergent: coefficient functions and operator condensates carry n! factorial growths that cancel only off-diagonally, never within a fixed power.