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

TL;DR

This paper systematically studies 4d $ abla=2$ S-folds in F-theory, classifying two infinite series of theories distinguished by discrete torsion and gauge bundle holonomy, and explores their properties using field and string theory methods.

Contribution

It introduces and analyzes two new infinite series of 4d $ abla=2$ S-fold theories with different discrete torsion and holonomy, expanding the understanding of F-theory 7-brane configurations.

Findings

Classification of two infinite series of S-fold theories.

Identification of differences based on discrete torsion and holonomy.

Analysis of properties using diverse theoretical methods.

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.