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 [1, 2] by {mathcal{S}}_{G,mathrm{ell}}^{(r)} for ℓ = 2, 3, 4 and {mathcal{T}}_{G,mathrm{ell}}^{(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.
Highlights
In [1, 2], one of the authors (Giacomelli) and his collaborators, generalized these constructions by considering fluxful S-folds of F-theory 7-branes
We summarize the properties of these theories in table 3. They have flavor symmetry of the form H × SU(2) when = 2 or H × U(1) when = 2, where H is a subgroup of G fixed by a certain order- automorphism, and SU(2) or U(1) come from the hyperkahler isometry
Our analysis strongly suggests that both SG(r,) and TG(r, ) admits a discrete gauging by a Z symmetry, which always acts non-trivially on the Higgs branch, while for TG(r, ) acts non-trivially on the Coulomb branch such that the operator of dimension r∆7 becomes of dimension r ∆7
Summary
The operation described above can be defined at the level of the F-theory Weierstrass model: we should consider a quotient of the Kodaira singularity describing the given 7brane which acts as a Z orbifold of the base of the Weierstrass fibration. We introduce the corresponding invariant coordinates X and Y , which are obtained by rescaling x and y by suitable powers of z, and require that Ω2 can be written in terms of X, Y and U only. These requirements imply that the invariant coordinates are. Where we have implicitly assumed that the Kodaira singularity can be rewritten in terms of the invariant coordinates only. This is possible only for solutions of (2.1).
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