Symmetry Mitosis and Hasse Diagram Diamonds: A Note on Brane Configurations with ${\mathrm{ON}}^0$ Planes

Abstract

This letter considers 3d $\mathcal{N}=4$ (unitary-)orthosymplectic quiver gauge theories originating from Type IIA and Type IIB brane systems with ${\mathrm{ON}}^0$ planes. Such theories lie outside the scope of present combinatorial techniques for Coulomb branch symmetry and symplectic stratification. It turns out that the correct prescription involves `symmetry mitosis': a common subset of nodes in two linear balanced chains source \emph{two} factors of a Coulomb branch global symmetry instead of one; the correct Coulomb branch Hasse diagram is obtained by a `doubling' procedure on that computed by naive quiver subtraction. Input from 6d SQFTs and little string theories allows for the construction of various `mitotic' magnetic quivers. The full Higgs branch Hasse diagram of minimal $(E_6,E_6)$ conformal matter is given. Additionally, a new Type I${}^{\prime }$ brane system using eight full D8 branes, negatively charged D6 branes, and ${\mathrm{ON}}^0$ planes is found corresponding to a product of $\mathrm{Spin}(32)$ instantons on ${\mathbb{C}}^2$. The corresponding 6d theory uses $\mathrm{Sp}(-1)$ gauge nodes which have the interpretation of bi-spinor matter of $\mathrm{O}(a)$ and $\mathrm{O}(12-a)$ for $a=0,1,\cdots ,12$.