Running Coupling for Holographic QCD with Heavy and Light Quarks: Isotropic case

TL;DR

This paper investigates the behavior of the running coupling constant in holographic QCD models with heavy and light quarks, analyzing its dependence on temperature and chemical potential through boundary conditions on the dilaton field.

Contribution

It introduces two boundary conditions for the dilaton field in holographic models and explores their effects on the running coupling and phase transition behavior.

Findings

The phase transition location does not depend on dilaton boundary conditions.

The running coupling exhibits jumps at phase transitions depending on temperature and chemical potential.

Under certain boundary conditions, the coupling decreases with increasing temperature and depends on a single variable in the QGP phase.

Abstract

We consider the running coupling constant in holographic models supported by Einstein-dilaton-Maxwell action for heavy and light quarks. To obtain the dependence of the running coupling constant $\alpha$ on temperature and chemical potential we impose boundary conditions on the dilaton field that depend on the position of the horizon. We use two types of boundary conditions: a simple boundary condition with the dilaton field vanishing at the horizon and a boundary condition that ensures an agreement with lattice calculations of string tension between quarks at zero chemical potential. The location of the 1st order phase transitions in $(\mu,T)$-plane does not depend on the dilaton boundary conditions for light and heavy quarks. At these phase transitions, the function $\alpha$ undergoes jumps depending on temperature and chemical potential. We also show that for the second boundary conditions the running coupling decreases with a temperature increase, and the dependence on temperature and chemical potential both for light and heavy quarks is actually specified in QGP phase by functions of one variable, demonstrating in this sense auto-model behavior.