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

Abstract

In this work, we investigate the effects of logarithms on the asymptotic behavior of power expansion/OPE in supper-renormalizable QFTs. We performed a careful investigation of the large $p^2$ expansion of a scalar-scalar two-point function at the next-to-leading order in the large-$N$ expansion, in a large-$N$ $O(N)$ quartic model that is populated by logarithms. We show that because the large-$p^2$ logarithms of the individual bubbles can be amplified by bubble-chains, there are factorial enhancements to the power expansion. We show how the factorial enhancements appear separately in the coefficient functions and operator condensates, and demonstrate how they are cancelled off-diagonally across different powers. Restricted to any given power, the factorial enhancements are no-longer canceled. The large-$p^2$ power expansion is divergent.