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

TL;DR

This paper explores 3d $ ext{N}=4$ orthosymplectic quiver gauge theories from brane systems with $ ext{ON}^0$ planes, introducing 'symmetry mitosis' to accurately determine Coulomb branch structures and presenting new brane configurations and Higgs branch diagrams.

Contribution

It introduces the concept of 'symmetry mitosis' for Coulomb branch analysis and constructs novel brane systems and magnetic quivers related to $ ext{ON}^0$ planes.

Findings

Full Higgs branch Hasse diagram of minimal $(E_6,E_6)$ conformal matter provided.

New Type I$'$ brane system with D8, D6, and $ ext{ON}^0$ planes identified.

Symmetry mitosis improves the accuracy of Coulomb branch symmetry computations.

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$'$ 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 $a=0,1,\cdots,12$.