More on $\mathcal{N} =2$ S-folds

Abstract

We carry out a systematic study of 4d $\mathcal{N} = 2$ preserving S-folds of F-theory 7-branes and the worldvolume theories on D3-branes probing them. They consist of two infinite series of theories, which we denote following the original 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 in the discrete torsion carried by the S-fold and in the difference in the asymptotic holonomy of the gauge bundle on the 7-brane. We study various properties of these theories, using diverse field theoretical and string theoretical methods.

Figures (21)

• Figure 1: Graphical depiction of the RG-relations among the ${\cal T}$ and ${\cal S}$ theories for $\ell=2$, $3$ and $4$. Entries in green, ${\color{green!60!black}{{\cal S}^{(r)}_{\varnothing,\ell=3,4}}}$ and ${\color{green!60!black}{{\cal S}^{(r)}_{\varnothing,\ell=3,4}}}$, are ${\mathcal{N}}=3$ supersymmetric, while entries in blue, ${\color{blue}{{\cal S}^{(r)}_{\varnothing,2}}}$ and ${\color{blue}{{\cal T}^{(r)}_{\varnothing,2}}}$, are ${\mathcal{N}}=4$ super Yang-Mills with gauge group $SO(2r+1)$ and $SO(2r)$, respectively. We also spelled out the rank-1 theories ${\mathcal{S}}^{(1)}_{G,\ell}$ and ${\mathcal{T}}^{(1)}_{G,\ell}$ using the standard notation $[\text{Kodaira type},\text{flavor symmetry}]$.
• Figure 2: ${\mathcal{N}}=2$ SCFTs which can be obtained by mass deforming rank-2 ${\mathcal{T}}$-theories. We displayed in yellow those which to our knowledge have not appeared in the literature before.
• Figure 3: Special Kähler stratification for ${\cal S}^{(2)}_{G,\ell}$, with $\ell=2,\ 3$ and $4$.
• Figure 4: $\ell=2$, 4 and 6.
• Figure 5: $\ell=3$ and 5.