A Pathway to Decay and Fission of Orthosymplectic Quiver Theories

We present an algorithm to extract the Coulomb branch Hasse diagram of orthosymplectic 3d $\mathcal{N}=4$ quiver gauge theories. The algorithm systematically predicts all descendant theories arising from Coulomb branch Higgsing, thereby detailing the stratification of the symplectic singularity defined by the initial Coulomb branch. Leveraging the Lie algebra isomorphism $\mathfrak{su}(4) \cong \mathfrak{so}(6)$, we validate our algorithm via the 3d mirror of 4d theories of class $\mathcal{S}$ of such type. This comparison involves moduli spaces that admit both orthosymplectic and unitary quiver realisations, the latter being well-understood via standard techniques such as Decay and Fission. Higgsing on the Coulomb branch of the 3d mirror or magnetic quiver translates to Higgs branch renormalization group flows of the corresponding higher-dimensional SCFTs. Thus, we benchmark our method via Higgsing 6d $\mathcal{N}=(1,0)$ D-type orbi-instanton theories, predicting novel Higgsing patterns involving products of interacting fixed points, and class $\mathcal{S}$ theories of type $\mathfrak{so}(2N)$, demonstrating Higgsing to products of theories of types specified by Levi subalgebras of $\mathfrak{so}(2N)$.