On brane systems with O+ planes — 5d and 6d SCFTs

Abstract

We study Higgs branches of field theories with 8 supercharges in 5 and 6 dimensions, focusing on theories realised on 5-brane webs in Type IIB with an O7⁺ plane, or a D6-D8-NS5 brane system in Type IIA in the presence of an O8⁺ plane. We find magnetic quivers for the Higgs branches of these theories. The main consequence of the presence of the orientifold is that it renders the magnetic quiver to be non-simply-laced. We propose a contribution of the O7⁺ to the usual stable intersection number of 5-branes from tropical geometry, and show that it is consistent with Fayet-Iliopoulos deformations of magnetic quivers which represent mass deformations of 5d SQFTs. From the magnetic quivers, we compute phase diagrams and highest weight generating functions for the Higgs branches, enabling us to identify the global form of the flavour symmetry for several families of 5d SQFTs; among them Bhardwaj’s rank-1 theory. For 6d theories realised on a −4 curve, we observe the appearance of an additional D₄ slice on top of the phase diagram as one goes to the tensionless limit.