Renormalization Group flows between Gaussian Fixed Points

TL;DR

This paper investigates non-perturbative renormalization group flows between different Gaussian fixed points in scalar theories, revealing continuous anomalous dimension changes and illustrating theories that are asymptotically free in both IR and UV.

Contribution

It demonstrates non-perturbative RG flows connecting multiple Gaussian fixed points with varying kinetic terms, highlighting the behavior of anomalous dimensions and free theories with diverging couplings.

Findings

Anomalous dimension varies continuously along RG flows.

Fixed points correspond to different free scalar theories with higher derivatives.

Diverging couplings can represent free theories in certain limits.

Abstract

A scalar theory can have many Gaussian (free) fixed points, corresponding to Lagrangians of the form $\phi\,\Box^k\phi$. We use the non-perturbative RG to study examples of flows between such fixed points. We show that the anomalous dimension changes continuously in such a way that at the endpoints the fields have the correct dimensions of the respective free theories. These models exhibit various pathologies, but are nonetheless interesting as examples of theories that are asymptotically free both in the infrared and in the ultraviolet. Furthermore, they illustrate the fact that a diverging coupling can actually correspond to a free theory.