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

Abstract

We carry out a systematic study of 4d $$ \mathcal{N} $$ 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 [1, 2] by $$ {\mathcal{S}}_{G,\mathrm{\ell}}^{(r)} $$ S G , ℓ r for ℓ = 2, 3, 4 and $$ {\mathcal{T}}_{G,\mathrm{\ell}}^{(r)} $$ T G , ℓ r for ℓ = 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.

S-fold magnetic quivers

“…In [4] it was argued that by moving along the ECB, the S (r) G, theories can be higgsed to another family of theories of the same rank, called T (r) G, . For = 2, this Higgsing can be described by activating a minimal nilpotent vacuum expectation value (VEV) for the moment map of the global symmetry of S (r) G,2 theories, specifically the global symmetry factor arising from the 7-brane of type G. It turns out that the T (r) G, models describe the theory on the world-volume of r D3 branes probing N = 2 S-folds without discrete flux [5,6].…”

“…The goal of quiver subtraction is to understand the Hasse diagram of the Coulomb branch of a quiver. 6 The rules of quiver subtraction have been explored for some years, however they are still elusive in full generality. So far these rules, and the interpretation of the quivers involved, were derived from Kraft-Procesi transitions in brane constructions, based on the classical Higgs mechanism, or through other empirical methods [28,41,42,75,76].…”

“…16t 2 + 30t 3 + 29t 4 − 40t 5 − 263t 6 − 476t 7 +277t 8 + 3930t 9 + 9560t 10 + O t 11 (−1 + t) 8 (1 + t) 6 (1 + t 2 ) 3 (1 + t + t 2 ) 4 7t 2 + 8t 3 + 8t 4 − 8t 5 − 31t 6 − 32t 7 +30t 8 + 168t 9 + 194t 10 + O t 11 (−1 + t) 10 (1 + t) 10 (1 + t 2 ) 5 (1 (−1 + t) 24 (1 + t) 22…”

“…This paper aims to study the Higgs branch of 4d N = 2 superconformal field theories (SCFTs) defined as the world-volume theories on D3 branes probing certain Type IIB backgrounds called S-folds [1][2][3][4][5][6]. At rank 1 these theories are well known; they were constructed through compactifications of 6d N = (1, 0) theories in [7][8][9], their Coulomb JHEP02(2021)054 branches were studied in detail [10][11][12][13][14][15], and their Higgs branches were recently studied through magnetic quivers in [16].…”

“…1 − 2t + 3t 2 + 2t 4 + 3t 6 − 2t 7 + t 8 (−1 + t) 6 (1 + t) 4 (1 + t 2 ) 2 4t 2 + 4t 3 + 7t 4 + 4t 5 − 5t 6 − 16t 7 −31t 8 − 20t 9 + 30t 10 + O t 11 (−1 + t) 12 (1 + t) 12 (1 + t 2 ) 6…”