Coupling renormalization flow in the strongly interacting regime of an asymptotically free quantum field theory in four dimensions

TL;DR

This paper numerically solves a four-dimensional scalar quantum field theory with $O(N)^3$ symmetry in the large-N limit, demonstrating stable strong interactions and a well-defined infrared flow, contrasting with perturbative predictions.

Contribution

It provides a closed-form numerical solution for an asymptotically free scalar QFT in four dimensions, revealing stable strong coupling behavior in the infrared regime.

Findings

The theory is asymptotically free with a stable, real effective action.

The coupling remains well-defined in the infrared, unlike in QCD.

Demonstrates dynamical build-up of strong interactions as correlation length increases.

Abstract

We consider a scalar quantum field theory with global $O(N)^3$ symmetry in four Euclidean dimensions and solve it numerically in closed form in the large-N limit. For imaginary tetrahedral coupling the theory is asymptotically free, with stable and real quantum effective action. We demonstrate the dynamical build-up of a strong interaction as the correlation length increases in a regime where the coupling renormalization flow remains well defined in the infrared. This is in contrast to perturbative results of asymptotically free theories, which predict that the coupling becomes ill-defined in the infrared, like in quantum chromodynamics. These properties make the model an important laboratory for the study of strong-coupling phenomena in quantum field theory from first principles.