QCD with an Infrared Fixed Point -- Pion Sector

The possibility that gauge theories with chiral symmetry breaking below the conformal window exhibit an infrared fixed point is explored. With this assumption three aspects of pion physics are reproduced if the the quark mass anomalous dimension at the infrared fixed point is $\gamma_* = 1$: First, by matching the long-distance scalar adjoint correlation function. Second, by perturbing the fixed point by a small quark mass, the $m_q$-dependence of the pion mass is reproduced by renormalisation group arguments. Third, consistency of the trace anomaly and the Feynman-Hellmann theorem, for small $m_q$, imply the same result once more. This suggests the following picture for the conformal window: close to its upper boundary $\gamma_*$ is zero and grows as the number of fermions is reduced until its lower boundary $\gamma_*=1$ is reached, where chiral symmetry breaking sets in. Below, the strongly coupled gauge theory with $\gamma_*=1$ is infrared dual to the free theory of pions. A possible dilaton sector of the scenario will be addressed in a companion paper.