Correlator of Wilson and t'Hooft Loops at Strong Coupling in $\mathcal{N}=4$ SYM Theory

We calculate the correlator of a 't Hooft and a Wilson coplanar circular concentric loops at strong coupling in N=4 SYM theory when it reduces to the calculation of the composite minimal surface in the curved space with the proper boundary conditions. The minimal admissible ratio of the radii of 't Hooft and Wilson loops for such a configuration is found to be $\mathrm{e}^{-1/2}\approx 0.606$ at zero temperature and the dependence of the minimal admissible radii ratio on temperature is derived. At low temperatures the minimal admissible ratio for 't Hooft and Wilson loops remains close to 0.6, whereas at high temperatures $T$ it becomes equal to $\frac{1}{\pi T}$. We find that at any temperature there exists a phase transition point: beneath some specific value of 't Hooft loop radius the dual counterpart of Wilson-'t Hooft correlator is organized as two disconnected surfaces in AdS, whereas for 't Hooft loop radius above it, there exists a connected configuration with a junction of monopole, charge and dyon surfaces. We suggest a generalization of the entanglement entropy for charged boundaries and make some comments on its calculation at strong coupling.