Beta-function dependence on the running coupling in holographic QCD models

We study the dependence of the beta-function on the running coupling constant in holographic models supported by the Einstein–dilaton–Maxwell action for light and heavy quarks. The dilaton defines the running coupling of the models. Its dependence on boundary conditions leads to the running coupling dependence on them. However, the behavior of the $\beta$-function as a function of the running coupling does not depend significantly on the boundary condition. The corresponding $\beta$-functions are negative and monotonically decreasing functions, and have jumps at first-order phase transitions for both light and heavy quarks. In addition, we compare our holographic results for the $\beta$-function as a function of the running coupling with perturbative results obtained within $2$-loop calculations.