Analytic Study of Magnetic Catalysis in Holographic QCD

We explore the effect of the magnetic field on the QCD phase transition through AdS/CFT correspondence. By introducing an anisotropic magnetic field in the Einstein-Maxwell-Scalar system, a family of analytic solutions is obtained by the potential reconstruction method where the contribution of the magnetic field in the blackening background can be analytically derived. After imposing the kinetic gauge function by requesting the linear Regge spectrum of $J/\psi$ mesons, the contribution of the magnetic field phase diagram can be demonstrated. The results show that the transition temperature will be raising as the magnetic field increases, which is the so-call magnetic catalysis effect. However, if the system is in a strong enough magnetic environment, the transition temperature will be cool down and display the inverse catalysis effect.