On Three-Dimensional Quiver Gauge Theories of Type B

TL;DR

This paper explores three-dimensional supersymmetric quiver gauge theories with non-simply laced symmetries, focusing on affine B_N quivers, S-duality transformations, and their implications for mirror symmetry and superconformal indices.

Contribution

It introduces a new framework for understanding 3D quiver gauge theories with affine B_N symmetry, including S-duality effects and a formula for superconformal indices.

Findings

Partition function transformation under S-duality studied.

Conjecture of generalized 3D mirror symmetry for nontrivial Chern-Simons theories.

Proposed superconformal index formula for affine B_N quiver theories.

Abstract

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 $SO(2N+1)$ 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.