't Hooft's construction of free energy, electric and magnetic fluxes, and of the partition function with twisted boundary conditions, is extended to the case of N = 4 supersymmetric Yang-Mills theories based on arbitrary compact, simple Lie groups. The transformation of the fluxes and the free energy under S-duality is presented. We consider the partition function of N = 4 for a particular choice of boundary conditions, and compute exactly its leading infrared divergence. We verify that this partition function obeys the transformation laws required by S-duality. This provides independent evidence in favor of S-duality in N = 4 theories.
ASJC Scopus subject areas
- Nuclear and High Energy Physics