3d dualities with decoupled sectors and brane transitions

TL;DR

This paper discovers exact relations among sphere partition functions of 3D $ ext{N}=4$ superconformal Chern-Simons theories, revealing new dualities involving decoupled sectors and brane transitions, using localization and Fermi gas methods.

Contribution

It introduces novel dualities combining circular and linear quiver gauge theories, interpreted as unique brane transitions beyond standard Hanany-Witten moves.

Findings

Exact relations among sphere partition functions were derived.

New dualities involving decoupled sectors were proposed.

Brane transitions extend beyond known Hanany-Witten and SL(2,Z) transformations.

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.