S-DUALITY IN N=4 YANG-MILLS THEORIES WITH GENERAL GAUGE GROUPS

't Hooft's construction of free energy, electric and magnetic fluxes, and of the partition function with twisted boundary conditions, is ext ended to the case of N = 4 supersymmetric Yang-Mills theories based on arbitrary compact, simple Lie groups. The transformation of the fluxe s and the free energy under S-duality is presented, We consider the pa rtition function of N = 4 for a particular choice of boundary conditio ns, and compute exactly its leading infrared divergence, We verify tha t this partition function obeys the transformation laws required by S- duality. This provides independent evidence in favor of S-duality in N = 4 theories.