Orthosymplectic quotient quiver subtraction

Abstract

The technique of orthosymplectic quotient quiver subtraction is introduced. This involves subtraction of an orthosymplectic quotient quiver from a 3d \( \mathcal{N} \) = 4 orthosymplectic quiver gauge theory which has the effect of gauging subgroups of the IR Coulomb branch global symmetry. Orthosymplectic quotient quivers for SU(2), SU(3), G₂, and SO(7) are found and derived from Type IIA brane systems involving negatively charged branes for certain 6d \( \mathcal{N} \) = (1, 0) gauge theories. Orthosymplectic quotient quiver subtraction is applied to magnetic quivers for nilpotent orbit closures providing new orthosymplectic counterparts to known unitary quivers. New Coulomb branch constructions are found such as for two height four nilpotent orbit closures of F₄ and one of height three. A novel application is to find magnetic quivers and Type IIA brane systems for the 6d \( \mathcal{N} \) = (1, 0) worldvolume theory of two \( \frac{1}{2}\textrm{M}5 \) branes on E₆ Klein singularity and for 6d \( \mathcal{N} \) = (1, 0) (E₆, E₆) conformal matter. These give a perturbative Lagrangian realisation to the dynamics of strongly interacting M5 branes. The magnetic quiver for 6d \( \mathcal{N} \) = (1, 0) (E₆, E₆) conformal matter is star-shaped and can also be interpreted as a magnetic quiver for a class \( \mathcal{S} \) theory specified by SO(26) algebra on a three-punctured sphere.