Renormalon-like factorial enhancements to power expansion/OPE in a super-renormalizable 2D O(N) quartic model

In this work, we investigate the power-expansion/OPE in super-renormalizable QFTs. In comparison to "marginal" short distance asymptotics, the power-expansion in super-renormalizable theory has a higher level of correlation with the coupling constant expansion, and the fixed-point perturbation theory for the coefficient functions suffers increasing level of IR divergences when the order of power-expansion/coupling constant expansion increases. This increasing IR sensitivity anticipates the presence of vacuum condensates of non-trivial local operators in the OPE, which not only cancel the IR divergences for coefficient functions through their UV divergences, but also shape the structure of logarithms at each power in the power-expansion. This UV-IR correspondence has been used to argue for the renormalon cancellation between coefficient functions and operators in marginal asymptotics, where the residue IR sensitivity of coefficient functions to be canceled by the operators manifests through high-order factorial growths after renormalization subtraction. However, in supper-renomalizable theory, high-order behavior in coupling constants in the coefficient functions is simultaneously large-order behavior in the power expansion, and one may wonder if there are also factorial growths for high-order/power terms in the coefficient functions, as they also require large-numbers of IR subtractions. In this work, we address the issue regarding the asymptotic behavior of power-expansion/OPE in supper-renormalizable theory. Using an O(N) quartic model at the next-to-leading order in the large-N expansion, we show that there are indeed factorial enhancements to high power terms in the coefficient functions. In the fixed-point perturbation theory, the factorial enhancements are introduced by the IR subtractions. Moreover, there are also factorial enhancements to the operator condensates, and the factorial enhancements cancel between coefficient functions and operators only off-diagonally across different powers. The observed factorial enhancements imply the divergence of the momentum-space power expansion.