Beta-Function Dependence on Running Coupling in Holographic QCD Models

TL;DR

This paper investigates how the beta-function depends on the running coupling in holographic QCD models, comparing results with perturbative calculations and analyzing phase transition effects.

Contribution

It provides a detailed analysis of beta-function behavior in Einstein-dilaton-Maxwell holographic models, showing independence from boundary conditions and identifying phase transition impacts.

Findings

Beta-functions are negative and monotonically decreasing.

Beta-functions exhibit jumps at first-order phase transitions.

Holographic results align with 2-loop perturbative calculations.

Abstract

We study the dependence of beta-function on running coupling constant in holographic models supported by Einstein-dilaton-Maxwell action for light and heavy quarks. Although, in the previous paper [arXiv:2402.14512], we considered different types of the dilaton boundary conditions, but since the behavior of $\beta$-function as a function of running coupling does not depend significantly on the boundary condition, we chose one. The corresponding $\beta$-functions are negative and monotonically decreasing functions, and have jumps on the 1-st order phase transitions for both light and heavy quarks. In addition, we compare our holographic results for $\beta$-function as a function of running coupling with perturbation results that obtained within 2-loop calculations.