2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/189643We investigate the 1/2-BPS Wilson-'t Hooft loops in ${\cal N}=4$ Super-Yang-Mills theory. We use the bulk D-brane with both electric and magnetic charges to calculate the all genus contribution of the circular loops. The expectation value of Wilson-'t Hooft loops are in perfect agreement with the result through supersymmetric condition and duality transformation in the gauge theory.20 pages, JHEP3 class;v2:Typos corrected,a misstatement corrected;v3:minor changes,full $SL(2,Z)$ duality completedHigh Energy Physics - Theorytext