Hecke Operator and S-Duality of N=4 Super Yang-Mills for ADE Gauge Group on K3

Physics – High Energy Physics – High Energy Physics - Theory

Scientific paper

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19 pages, typo corrections, references added

Scientific paper

10.1088/1126-6708/2003/07/024

We determine the partition functions of ${\cal N}=4$ super Yang-Mills gauge theory for some $ADE$ gauge groups on $K3$, under the assumption that they are holomorphic. Our partition functions satisfy the gap condition and Montonen-Olive duality at the same time, like the SU(N) partition functions of Vafa and Witten. As a result we find a close relation between Hecke operator and $S$-duality of ${\cal N}=4$ super Yang-Mills for $ADE$ gauge group on $K3$.

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