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

TL;DR

This paper investigates S-duality in orientifolds of Calabi-Yau cones over the first del Pezzo surface, revealing intrinsically strongly-coupled sectors that are crucial for understanding such dualities and their associated gauge theories.

Contribution

It introduces a method to construct and analyze strongly-coupled sectors in $dP_1$ orientifolds using deconfinement, advancing the understanding of S-duality in these complex systems.

Findings

Identified strongly-coupled sectors as intersections of NS5 and D5 branes at infinite coupling.

Constructed these sectors explicitly for $dP_1$ orientifolds.

Verified S-duality predictions using the constructed sectors.

Abstract

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 $dP_1$.