Scale Separation, Strong Coupling UV Phases, and the Identification of the Edge of the Conformal Window

Abstract: We use a simple holographic model to discuss approaching the edge of the conformal window in strongly coupled gauge theories to draw lessons for lattice studies. Walking gauge theories have a gap between the scale where they enter the strong coupling regime and the scale of chiral symmetry breaking. We highlight that there can also be a gap between the scale where the critical value of the quark anti-quark operator's anomalous dimension is passed and the scale of the condensate. This potentially makes identifying the edge of the conformal window in a lattice simulation with UV bare coupling below the fixed point value on a finite lattice difficult. A resolution is to study the theory with a coupling above the fixed point value at the UV cut off. Here we show that an ``artefact" phase with chiral symmetry breaking triggered at the UV cut off exists and lies arbitrarily close to the fixed point at the edge of the conformal window. We quantify the chance of a misidentification of a chiral symmetry breaking theory as IR conformal. We also quantify where the artefact phase lies, tuned to the fixed point value. We use the latest lattice results for SU(3) gauge theory with ten quark flavours in [Hasenfratz:2023wbr] as a test case; we conclude their identification that the theory is in the conformal window is reliable.