Hyper-Scaling Relations in the Conformal Window from Dynamic AdS/QCD

TL;DR

This paper uses a holographic model to study the scaling relations of meson masses and decay constants in strongly coupled gauge theories with massive quarks within the conformal window, incorporating flavor decoupling effects.

Contribution

It introduces a method to include quark flavor decoupling in the Dynamic AdS/QCD model, enabling the calculation of mesonic spectra and their scaling behaviors in the conformal window.

Findings

The model reproduces perturbative behavior for large quark masses.

It aligns with naive dimensional analysis at small quark masses.

Provides insights into intermediate regimes with multiple scales.

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, gamma. We apply it to describe the physics of massive quarks in the conformal window of SU(N_c) gauge theories with N_f fundamental flavours, assuming the perturbative two loop running for gamma. We show that to find regular, holographic, renormalization group flows in the infra-red the decoupling of the quark flavours at the scale of the mass is important and enact it through suitable boundary conditions when the flavours become on shell. We can then compute the quark condensate and the mesonic spectrum (M_rho, M_pi, M_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 naive 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.