Hyper-scaling relations in the conformal window from dynamic AdS/QCD

Abstract

Dynamic AdS/QCD is a holographic model of strongly coupled gauge theories with the dynamics included through the running anomalous dimension of the quark bilinear, $\ensuremath{\gamma}$. We apply it to describe the physics of massive quarks in the conformal window of $\mathrm{SU}({N}_{c})$ gauge theories with ${N}_{f}$ fundamental flavors, assuming the perturbative two-loop running for $\ensuremath{\gamma}$. We show that to find regular, holographic renormalization group flows in the infrared, the decoupling of the quark flavors at the scale of the mass is important, and enact it through suitable boundary conditions when the flavors become on shell. We can then compute the quark condensate and the mesonic spectrum $({M}_{\ensuremath{\rho}},{M}_{\ensuremath{\pi}},{M}_{\ensuremath{\sigma}})$ and decay constants. We compute their scaling dependence on the quark mass for a number of examples. The model matches perturbative expectations for large quark mass and na\"{\i}ve dimensional analysis (including the anomalous dimensions) for small quark mass. The model allows study of the intermediate regime where there is an additional scale from the running of the coupling, and we present results for the deviation of scalings from assuming only the single scale of the mass.