A misleading Wilsonian fixed point

TL;DR

This paper reveals a Wilsonian fixed point in a scalar theory that appears non-trivial but actually describes a free theory, highlighting subtleties in functional methods in Quantum Field Theory.

Contribution

It demonstrates a case where a Wilsonian fixed point is misleadingly non-trivial yet corresponds to a free theory, clarifying interpretational issues.

Findings

Identifies a Wilsonian fixed point that describes a free theory

Highlights potential misinterpretations in functional methods

Contributes to understanding fixed points in scalar theories

Abstract

We exhibit here, for a scalar theory, an apparently non-trivial Wilsonian fixed point, which surprisingly describes a free theory. This modest note is an observation which can be of interest in the framework of functional methods in Quantum Field Theory.