Domain Wall and Three Dimensional Duality

TL;DR

This paper investigates 1/2 BPS domain walls in 3d N=4 supersymmetric gauge theories, demonstrating how duality transformations exchange charges and topological features, especially with BF couplings, revealing classical invariance.

Contribution

It provides a detailed analysis of domain wall invariance under 3d mirror symmetry, explicitly showing charge exchanges and the role of BF couplings in classical BPS equations.

Findings

Charges and vortex topological charges are correctly exchanged under duality.

BF-type couplings enable explicit classical invariance of domain walls.

The duality swaps particles and vortices in the context of domain walls.

Abstract

We discuss 1/2 BPS domain walls in the 3d $\mathcal N=4$ supersymmetric gauge theory which is self-dual under the 3d mirror symmetry. We find that if a BF-type coupling is introduced, invariance of the BPS domain wall under the duality transformation can be explicitly seen from the classical BPS equations. It has been known that particles and vortices are swapped under the 3d duality transformations. We show that Noether charges and vortex topological charges localized on the domain walls are correctly exchanged under the 3d mirror symmetry.