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S-Duality in N=4 Yang-Mills Theories with General Gauge Groups,

Luciano Girardello·Amit Giveon·Massimo Porrati·Alberto Zaffaroni
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Abstract

't Hooft 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.

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Luciano Girardello, Amit Giveon, Massimo Porrati, Alberto Zaffaroni. 1995-02-09. S-Duality in N=4 Yang-Mills Theories with General Gauge Groups,. https://doi.org/10.1016/0550-3213(95)00177-t

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