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We calculate the correlator of a 't Hooft and a Wilson coplanar circularconcentric loops at strong coupling in N=4 SYM theory when it reduces to thecalculation of the composite minimal surface in the curved space with theproper boundary conditions. The minimal admissible ratio of the radii of 'tHooft 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 theminimal admissible radii ratio on temperature is derived. At low temperaturesthe minimal admissible ratio for 't Hooft and Wilson loops remains close to0.6, whereas at high temperatures $T$ it becomes equal to $\frac{1}{\pi T}$. Wefind that at any temperature there exists a phase transition point: beneathsome specific value of 't Hooft loop radius the dual counterpart of Wilson-'tHooft correlator is organized as two disconnected surfaces in AdS, whereas for't Hooft loop radius above it, there exists a connected configuration with ajunction of monopole, charge and dyon surfaces. We suggest a generalization ofthe entanglement entropy for charged boundaries and make some comments on itscalculation at strong coupling.

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