Orthosymplectic Quotient Quiver Subtraction

TL;DR

The paper introduces orthosymplectic quotient quiver subtraction, a new technique for analyzing 3d N=4 orthosymplectic gauge theories, deriving new quivers and brane systems, and providing insights into M5 branes and conformal matter.

Contribution

It develops orthosymplectic quotient quiver subtraction and applies it to construct new Coulomb branch quivers and brane systems for complex gauge theories.

Findings

Derived orthosymplectic quotient quivers for SU(2), SU(3), G2, SO(7).

Constructed magnetic quivers for nilpotent orbit closures and 6d theories.

Linked magnetic quivers to Type IIA brane systems and class S theories.

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 $\mathrm{SU}(2),\;\mathrm{SU}(3),\;G_2,$ and $\mathrm{SO}(7)$ 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 $F_4$ 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 $\frac{1}{2}$M5 branes probing $E_6$ Klein singularity and for $6d\;\mathcal N=(1,0)\;(E_6,E_6)$ conformal matter. These give a perturbative Lagrangian realisation to the dynamics of strongly interacting M5 branes. The magnetic quiver for $6d\;\mathcal N=(1,0)\;(E_6,E_6)$ conformal matter is star-shaped and can also be interpreted as a magnetic quiver for a class $\mathcal S$ theory specified by $\mathrm{SO}(26)$ algebra on a three-punctured sphere.