Beta-Functions and RG flows for Holographic QCD with Heavy and Light Quarks: Isotropic case

In a previous paper [arXiv:2402.14512v3], we investigated the dependence of the running coupling constant on temperature and chemical potential for holographic models of the light and heavy quarks, supported by an Einstein-dilaton-Maxwell action. In this paper, we study the dependence of the corresponding $\beta$-functions on the temperature and the chemical potential. As in the previous paper, we give special attention to the behavior of the $\beta$-functions near the 1st order phase transitions. We consider different types of boundary conditions for the dilaton. Only one of the possible boundary conditions yields results that agree with lattice calculations at zero chemical potential. The corresponding $\beta$-functions are negative and exhibit jumps at the 1st order phase transitions. We also show that the RG fluxes are invariant with respect to the choice of the boundary conditions and that our exact solutions for the light and heavy quarks are unstable, as expected, given their negative dilaton potentials.