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

TL;DR

This paper studies how logarithmic effects cause factorial enhancements in the power expansion of a super-renormalizable 2D $O(N)$ model, revealing divergence due to amplified logarithms in bubble chains.

Contribution

It demonstrates the emergence of factorial enhancements in the power expansion of a 2D $O(N)$ model caused by logarithms and bubble chains, a novel insight into divergence mechanisms.

Findings

Factorial enhancements arise from amplified logarithms in bubble chains.

These enhancements are canceled across different powers but persist within individual powers.

The large-$p^2$ power expansion is divergent due to these effects.

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.