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We carry out a systematic study of 4d $\mathcal{N} = 2$ preserving S-folds ofF-theory 7-branes and the worldvolume theories on D3-branes probing them. Theyconsist of two infinite series of theories, which we denote following theoriginal papers by $\mathcal{S}^{(r)}_{G,\ell}$ for $\ell = 2,3,4$ and$\mathcal{T}^{(r)}_{G,\ell}$ for $\ell = 2,3,4,5,6$. Their distinction lies inthe discrete torsion carried by the S-fold and in the difference in theasymptotic holonomy of the gauge bundle on the 7-brane. We study variousproperties of these theories, using diverse field theoretical and stringtheoretical methods.

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