Life at the Landau pole

TL;DR

This paper investigates the nature of the Landau pole in a 4d O(N) model, revealing that it is benign and does not affect physical observables, challenging the traditional view of Landau poles as problematic.

Contribution

It demonstrates that in the 4d O(N) model at large N, the Landau pole does not lead to divergences in physical observables, and explores deformations at the pole.

Findings

Observables remain finite at the Landau pole.

Deformations do not alter physical predictions at the pole.

The Landau pole is benign in this model.

Abstract

If a quantum field theory has a Landau pole, the theory is usually called 'sick' and dismissed as a candidate for an interacting UV-complete theory. In a recent study on the interacting 4d O(N) model at large N, it was shown that at the Landau pole, observables remain well-defined and finite. In this work, I study both relevant and irrelevant deformations of the said model at the Landau pole, finding that physical observables remain unaffected. Apparently, the Landau pole in this theory is benign. As a phenomenological application, I compare the O(N) model to QCD, by identifying $\Lambda_{\overline{\rm MS}}$ with the Landau pole in the O(N) model.