On brane systems with O${}^+$ planes -- 5d and 6d SCFTs

TL;DR

This paper investigates Higgs branches of 5d and 6d supersymmetric theories realized on brane webs with orientifold planes, deriving magnetic quivers and analyzing their geometric and symmetry properties.

Contribution

It introduces non-simply-laced magnetic quivers for these theories and proposes a new contribution of O$7^+$ planes to stable intersection numbers, advancing the understanding of Higgs branches in these contexts.

Findings

Magnetic quivers are non-simply-laced due to orientifolds.

Proposed a tropical geometry contribution for O$7^+$ planes.

Identified global flavor symmetries and phase structures of 5d SQFTs.

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 O$7^+$ plane, or a D6-D8-NS5 brane system in Type IIA in the presence of an O$8^+$ 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 O$7^+$ 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 $D_4$ slice on top of the phase diagram as one goes to the tensionless limit.