Holographic QCD Running Coupling for Light Quarks in Strong Magnetic Field

We consider running coupling constant in holographic model with external magnetic field supported by Einstein-dilaton-three-Maxwell action. We obtain a significant dependence of the running coupling constant $\alpha$ on chemical potential, temperature and magnetic field. We use the boundary condition that ensures the 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. We observe that running coupling $\alpha$ decreases with increasing magnetic field for the fixed values of chemical potential and temperature. At the 1st order phase transitions the functions $\alpha$ undergo jumps depending on temperature, chemical potential and magnetic field.