Critical $O(2)$ and $O(3)$ $\phi^4$ theories near six dimensions

TL;DR

This paper introduces a new reformulation of $O(N)$ symmetric $^4$ theories near six dimensions, revealing IR-stable fixed points for low N, and suggests these models could be examples of asymptotically safe quantum field theories.

Contribution

It proposes a novel tensorial reformulation of $O(N)$ $^4$ theories that uncovers IR-stable fixed points near six dimensions for low N, advancing understanding of asymptotic safety.

Findings

IR-stable fixed points found near six dimensions for N=2,3

Reformulation in terms of tensorial fields with cubic and Yukawa interactions

Potential extension to five dimensions discussed

Abstract

We consider $O(N)$-symmetric bosonic $\phi^4$ field theories above four dimensions, and propose a new reformulation in terms of an irreducible tensorial field with a cubic and Yukawa terms. The $\phi^4$ field theory so rewritten exhibits real and nontrivial IR-stable fixed points near and below six dimension, for low values of $N$ such as $N=2$ and $N=3$. The so-defined UV completions of the $O(2)$ and $O(3)$ models hence constitute precious examples of asymptotically safe quantum field theories. The possibility of an extension of our results to five dimensions is discussed.