4d N=2 S -folds

Abstract

We propose a generalization of S-folds to 4d N = 2 theories. This construction is motivated by the classification of rank one 4d N = 2 super-conformal field theories (SCFTs), which we reproduce from D3-branes probing a configuration of N = 2 S-folds combined with 7-branes. The main advantage of this point of view is that realizes both Coulomb and Higgs branch flows and allows for a straight forward generalization to higher rank theories.

Magnetic quivers for rank 1 theories

“…This is in full agreement with the results of this section. Also, [7] correctly identifies that away from the origin the moduli space looks flat, which is consistent…”

“…The list of 17 SCFTs is presented in the right part of table 1. Alternatively, the theories can be obtained from Z k N = 2 Sfold constructions [7], from the compactification of (1, 0) 6d SCFTs with non-trivial global symmetry background [31], or from Z k twisted compactification from 5d N = 1 SCFTs, as detailed in section 4. This is the reason for the organization into rows and columns: the row gives the geometry of the Coulomb branch in the singular limit, and the column gives the Z k group.…”

“…In this case the pure Coulomb branch of the theory is contained as a subvariety in a mixed branch, which is called the enhanced Coulomb branch. This implies that there is a partial Higgsing from a rank 1 SCFT with an enhanced Coulomb branch, to a rank 1 SCFT where the Coulomb branch is not enhanced [7]. (Classical) Higgs branches of Lagrangian 4d N = 2 theories are constructed through the hyper-Kähler quotient [8][9][10].…”

3d mirrors of the circle reduction of twisted A2N theories of class S

“…The appearance of C 2 /Z 6 can be understood by considering the S-fold realization of the C 2 U 1 theory [64]: in the F-theory context this model arises by probing with a D3 brane a background which is obtained by combining a 7-brane of type H 2 with a Z 2 S-fold action whose effect is to act as a sign flip on the Coulomb branch of the H 2 (or (A 1 , D 4 )) theory resulting in a IV * geometry. Upon reduction to three dimensions the Coulomb branch of the (A 1 , D 4 ) theory becomes the hyperkahler singularity C 2 /Z 3 as we have seen before.…”

Classification of all $\mathcal{N}\geq 3$ moduli space orbifold geometries at rank 2

“…Strictly speaking, the term S-fold is reserved to m = 3, 4, 6; the case m = 1 corresponds to no identification at all, and m = 2 is an actual orientifold plane 18. Flux-less S-folds can give rise to genuinely new theories even at rank 2; the worldvolume theory on D3 branes probing the S-folds combined with exceptional sevenbranes gives rise to N = 2 SCFTs[43]. In this case the flux-less S-folds give genuinely new N = 2 SCFTs even in the presence of only two D3 probes[44][45][46] 19.…”