Symmetry mitosis and Hasse diagram diamonds: a note on brane configurations with ON0 planes

A bstract This letter considers 3d N N = 4 (unitary-)orthosymplectic quiver gauge theories originating from Type IIA and Type IIB brane systems with 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 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 ON 0 planes is found corresponding to a product of Spin(32) instantons on ℂ 2 . The corresponding 6d theory uses Sp(−1) gauge nodes which have the interpretation of bi-spinor matter of O( a ) and O(12 − a ) for a = 0, 1, · · · , 12.