On three-dimensional quiver gauge theories of type B

We study three-dimensional supersymmetric quiver gauge theories with a non-simply laced global symmetry primarily focusing on framed affine B-N quiver theories. Using a supersymmetric partition function on a three sphere, and its transformation under S-duality, we study the three-dimensional ADHM quiver for SO(2 N + 1) instantons with a half-integer Chern-Simons coupling. The theory after S-duality has no Lagrangian, and can not be represented by a single quiver, however its partition function can be conveniently described by a collection of framed affine B-N quivers. This correspondence can be conjectured to generalize three-dimensional mirror symmetry to theories with nontrivial Chern-Simons terms. In addition, we propose a formula for the superconformal index of a theory described by a framed affine B-N quiver.