Conformal symmetry of QCD in $d$-dimensions

TL;DR

This paper provides a technical proof that Quantum Chromodynamics (QCD) in non-integer dimensions at its critical point exhibits conformal symmetry, supporting the idea that scale invariance implies conformal invariance in this context.

Contribution

The paper offers a rigorous proof that QCD at its critical point in $d=4-2\epsilon$ dimensions is a conformal field theory, clarifying its symmetry properties.

Findings

QCD in $d=4-2\epsilon$ dimensions has a nontrivial critical point.

Scale invariance at the critical point implies conformal symmetry in QCD.

The proof confirms the conformal nature of QCD in this setting.

Abstract

QCD in $d=4-2\epsilon$ space-time dimensions possesses a nontrivial critical point. Scale invariance usually implies conformal symmetry so that there are good reasons to expect that QCD at the critical point restricted to the gauge invariant subsector provides one with an example of a conformal field theory. The aim of this letter is to present a technical proof of this statement which is important both as a matter of principle and for applications.