Low-energy theorem and OPE in the conformal window of massless QCD

We develop a new technique, based on a low-energy theorem (LET) of NSVZ type derived in arXiv:1701.07833, for the nonperturbative investigation of SU(N) QCD with Nf massless quarks - or, more generally, of massless QCD-like theories - in phases where the beta function, β(g), with g=g(μ) the renormalized gauge coupling, admits an isolated zero, g∗, in the infrared (IR) or ultraviolet (UV). We point out that the LET sets constraints on 3-point correlators involving the insertion of TrF2, its anomalous dimension γF2, and the anomalous dimensions of multiplicatively renormalizable operators at g∗. These constraints intertwine with the exact conformal scaling for g(μ)→g∗ with μ≠0,+∞ fixed and the IR/UV asymptotics - which may or may not coincide with the IR/UV limit of the aforementioned conformal scaling - for ΛIR/UV fixed. In the conformal case we also discuss how the LET for bare correlators is the rationale for the existence in massless QCD of the mysterious divergent contact term in the OPE of TrF2 with itself discovered in perturbation theory in arXiv:1209.1516, arXiv:1407.6921 and computed to all orders in arXiv:1601.08094. Specifically, if γF2 does not vanish, the divergent contact term in the rhs of the LET for the 2-point correlator of TrF2 has to match - and we verify by direct computation that it actually does - the divergence in the lhs due to the nontrivial anomalous dimension of TrF2. Hence, remarkably, the additive renormalization due to the divergent contact term in the rhs is related by the LET to the multiplicative renormalization in the lhs, in such a way that a suitably renormalized version of the LET has no ambiguity for additive renormalization.