Conformal symmetry of QCD in d-dimensions

Abstract

QCD in d=4−2ϵ space-time dimensions possesses a nontrivial critical point and there are good reasons to expect that this theory restricted to the gauge-invariant subsector is conformally invariant. The subtlety is that the conformal symmetry of the Lagrangian is broken by the Faddeev-Popov quantization procedure. We study this problem by tracing carefully the contributions of gauge non-invariant operators in conformal Ward identities and prove that all such contributions cancel in the correlation functions of gauge-invariant operators. This result gives further support to the application of the conformal symmetry based methods in high-order QCD calculations. Keywords: Conformal symmetry, Renormalization, QCD