Potential analysis of holographic Schwinger effect in the magnetized background

We study the holographic Schwinger effect with magnetic field at RHIC and LHC energies by using the AdS/CFT correspondence. We consider both weak and strong magnetic field cases with $B\ll T^2$ and $B\gg T^2$ solutions respectively. Firstly, we calculate separating length of the particle pairs at finite magnetic field. It is found that for both weak and strong magnetic field solutions the maximum value of separating length decreases with the increase of magnetic field , which can be inferred that the virtual electron-positron pairs become real particles more easily. We also find that the magnetic field reduces the potential barrier and the critical field for the weak magnetic field solution, thus favors the Schwinger effect. With strong magnetic field solution, the magnetic field enhances the Schwinger effect when the pairs are in perpendicular to the magnetic field although the magnetic field increases the critical electric field.