S-folds, String Junctions, and 4D $\mathcal{N} = 2$ SCFTs

Abstract

S-folds are a non-perturbative generalization of orientifold 3-planes which figure prominently in the construction of 4D N = 3 SCFTs and have also recently been used to realize examples of 4D N = 2 SCFTs. In this paper we develop a general procedure for reading off the flavor symmetry experienced by D3-branes probing 7-branes in the presence of an S-fold. We develop an S-fold generalization of orientifold projection which applies to non-perturbative string junctions. This procedure leads to a different 4D flavor symmetry algebra depending on whether the S-fold supports discrete torsion. We also show that this same procedure allows us to read off admissible representations of the flavor symmetry in the associated 4D N = 2 SCFTs. Furthermore this provides a prescription for how to define F-theory in the presence of S-folds with discrete torsion.

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

“…It is possible to use various properties of this SCFT, observed from the 5d construction, to argue that the dimensions of the Coulomb branch operators should be ∆ = { 5 2 , 3}. Specifically, we observe the following properties of this SCFT:…”

“…As here we expect the rank to remain two, the Coulomb branch spanning operators cannot be lifted, so must decompose to Coulomb branch operators of smaller dimension. It is straightforward to see that the only scenario consistent with the expected value of n v is that the dimension 5 Coulomb branch operator decomposes to the square of a dimension 5 2 Coulomb branch operator, leading to the Coulomb branch being spanned by operators of dimension 5 2 and 3. This conclusion is completely consistent with the 4d moduli space analysis presented below.…”

“…(6) 2 by the gauging. Then from (3.7c) immediately follows that the CB coordinate with the lowest scaling dimension should have ∆ u =5 2 , as argued above, and thatS U Sp(6) := {(u, v) ∈ C | u = 0}. (5.11) …”

Snowmass White Paper on SCFTs

“…The class-S theories, i.e., those which can be engineered by compactifying (2, 0) 6D theories on a Riemann surface in the presence of codimension-two defects [204][205][206][207][208][209][210][211][212][213][214][215][216][217][218][219][220][221] fill a vast landscape of SCFTs. More recently, a thorough understanding of the wordvolume theory of D3 branes in F-theory probing both an S-fold [222,223] a generalization of an orientifold -and an exceptional 7-brane singularity, the so-called N = 2 S-folds [223][224][225][226][227][228] has been used to move beyond class S. 3 This construction also realizes theories which had been predicted by the systematic analysis of rank-1 theories and which can be instead realized in the more general construction of twisted compactification of 6D (1, 0) theories [229]. The methods which worked to compile the classification in rank-1 are of limited use for higher ranks.…”

AdS$_5$ Holography and Higher-Derivative Supergravity

“…Note also that recently this class of models has been generalized to include the so-called S-folds. The conformal anomalies for these 4d N = 2 S-fold SCFTs were computed in [49][50][51] and can be directly used to derive the corresponding four-derivative supergravity couplings as we did above.…”