S‐duality in orientifold SCFTs

Abstract

We present a general solution to the problem of determining all S‐dual descriptions for a specific (but very rich) class of N=1 SCFTs. These SCFTs are indexed by decorated toric diagrams, and can be engineered in string theory by probing orientifolds of isolated toric singularities with D3 branes. The S‐dual phases are described by quiver gauge theories coupled to specific types of conformal matter which we describe explicitly. We illustrate our construction with many examples, including S‐dualities in previously unknown SCFTs.

Mass deformations of unoriented quiver theories

“…To this end, we will use various tools ranging from Quiver diagrams and, when toricity holds, Dimer and Toric diagrams. Unoriented toric singularities were already discussed in the Dimer literature and a number of anomaly-free models were found thanks to the identification of a set of rules for unoriented projections [22][23][24][25][26]. However, a Quiver description of these results was lacking and in the present work we are able to reproduce them by considering a generalization of the anomaly-cancellation equations previously used in [27].…”

“…More recently toric singularities [17,18], that admit global symmetries G ⊃ U(1) 2 in addition to U(1) R R-symmetry, have been studied, in particular those associated to 'reflexive' polygons [19][20][21]. Notwithstanding some important exceptions [22][23][24][25][26], the investigation of unoriented singularities has been much less systematic. In this case an orientation reversing action σ on the CY is combined with world-sheet parity Ω that entails an action γ Ω on the Chan-Paton factors or, equivalently, on the D-branes.…”

Global orientifolded quivers with inflation

“…In both cases we have a non-vanishing superpotential of the form W = ijk Tr(A i A j B k ). The resulting brane system sources no D7 or D5 charge, while sourcing (2N − 3)/2 units of mobile D3 charge (in the double cover) in the SO case, and (2N + 3)/2 units of mobile D3 charge in the USp case [15]. Our goal in this paper is to study these theories as examples for semi-realistic string constructions, so choosing the SO projection with N = 5 would seem optimal: we obtain a SU (5) theory with three generations of 5 and 10, reasonably reminiscent of conventional SU (5) GUT models, except for the absence of the corresponding Higgs boson.…”

2D CFT blocks for the 4D class S k $$ {\mathcal{S}}_k $$ theories

“…We refer to (10) and its surrounding paragraph for the definition of the curve coefficientsφ ℓ (t). We shall also see that (26) can be made to work also for the case without the shift in x. This requires the reintroduction of the decoupled U(1) degrees of freedom that on the CFT side are contained in the free boson field λ.…”

“…A very large class of 4D N = 1 SCFTs, naturally called S Γ [18,19], arise from M5-branes probing the C 2 /Γ ADE singularity. Their study was originated in [20], with the S k class arising after compactification of Z k orbifolds of the (2,0) theory, see also [21,22] and [18,[23][24][25][26][27]. The SW curves for the class S k theories were derived and studied in [28], using Witten's M-theory approach [29].…”