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arXiv · hep-th/9601059

$N=2$ Super Yang-Mills and Subgroups of $SL(2,Z)$

Joseph A. Minahan·Dennis Nemeschansky
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Abstract

We discuss $SL(2,Z)$ subgroups appropriate for the study of $N=2$ Super Yang-Mills with $N_f=2n$ flavors. Hyperelliptic curves describing such theories should have coefficients that are modular forms of these subgroups. In particular, uniqueness arguments are sufficient to construct the $SU(3)$ curve, up to two numerical constants, which can be fixed by making some assumptions about strong coupling behavior. We also discuss the situation for higher groups. We also include a derivation of the closed form $β$-function for the $SU(2)$ and $SU(3)$ theories without matter, and the massless theories with $N_f=n$.

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Joseph A. Minahan, Dennis Nemeschansky. 1996-02-01. $N=2$ Super Yang-Mills and Subgroups of $SL(2,Z)$. https://doi.org/10.1016/0550-3213(96)00167-8

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