Strongly coupled phases of N = 1 $$ \mathcal{N}=1 $$ S-duality

We analyze S-duality of orientifolds of the Calabi-Yau cone over the first del Pezzo surface ( dP 1 ). The S-duals of known phases, described by quiver gauge theories, contain intrinsically strongly-coupled sectors. These sectors are realized by a higher multiplicity intersection of NS5 branes and D5 branes atop an O5 plane, and can be thought of as stuck at the infinite coupling point between two Seiberg-dual gauge theories. We argue that such sectors appear generically in orientifolds of non-orbifold singularities, where in many examples every orientifold phase contains such a sector. Understanding such sectors is therefore key to understanding orientifolds of Calabi-Yau singularities. We construct the strongly-coupled sectors for dP 1 orientifolds using deconfinement, and show that they have interesting, non-trivial properties. Using this construction, we verify the predictions of S-duality for dP 1