Resizing the Conformal Window: A beta function Ansatz

TL;DR

This paper introduces a new ansatz for the nonperturbative beta function in non-supersymmetric Yang-Mills theories, predicting the conformal window and allowing for both infrared and ultraviolet fixed points.

Contribution

It presents a novel beta function ansatz that extends previous models by including an unstable ultraviolet fixed point, enhancing understanding of the conformal window in gauge theories.

Findings

Predicts the conformal window boundaries.

Identifies a merger point of fixed points at the conformal window's edge.

Allows for an ultraviolet fixed point alongside the infrared one.

Abstract

We propose an ansatz for the nonperturbative beta function of a generic non-supersymmetric Yang-Mills theory with or without fermions in an arbitrary representation of the gauge group. While our construction is similar to the recently proposed Ryttov-Sannino all order beta function, the essential difference is that it allows for the existence of an unstable ultraviolet fixed point in addition to the predicted Bank-Zaks -like infrared stable fixed point. Our beta function preserves all of the tested features with respect to the non-supersymmetric Yang-Mills theories. We predict the conformal window identifying the lower end of it as a merger of the infrared and ultraviolet fixed points.