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

Joseph A. Minahan; Dennis Nemeschansky

doi:10.1016/0550-3213(96)00167-8

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

High Energy Physics - Theory 2009-10-30 v2

Authors: 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 $\beta$ -function for the $SU(2)$ and $SU(3)$ theories without matter, and the massless theories with $N_f=n$ .

Keywords

n=2 super yang-mills sl(2,z) subgroups hyperelliptic curves modular forms su(3) curve beta function

Cite

@article{arxiv.hep-th/9601059,
  title  = {$N=2$ Super Yang-Mills and Subgroups of $SL(2,Z)$},
  author = {Joseph A. Minahan and Dennis Nemeschansky},
  journal= {arXiv preprint arXiv:hep-th/9601059},
  year   = {2009}
}

Comments

harvmac, 16 pages, no figures. (Expressions for beta functions have been simplified. Minor corrections in text)

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

Abstract

Keywords

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