3d dualities with decoupled sectors and brane transitions

Abstract

We find exact relations among the sphere partition functions of three-dimensional $\mathcal{N}=4$ superconformal Chern-Simons theories with circular quiver diagrams. These relations suggest new dualities in gauge theories which are the products of circular quiver gauge theories and decoupled linear quiver gauge theories. The dualities can be interpreted as simple brane transitions in the Hanany-Witten brane construction in type IIB string theory. Interestingly, the brane transitions cannot be generated by the Hanany-Witten transition or the ${\rm SL}\left(2,\mathbb{Z}\right)$ transformation. Our results can be regarded as generalization and clarification of dualities implied from Weyl symmetries of quantum curves. To obtain the exact results, we employ the supersymmetric localization technique and the Fermi gas approach.