(2,2) and (0,4) Supersymmetric Boundary Conditions in 3d N = 4 Theories and Type IIB Branes

TL;DR

This paper classifies and analyzes half-BPS boundary conditions preserving specific supersymmetries in 3d N=4 theories, connecting them to brane configurations in Type IIB string theory.

Contribution

It provides a detailed study of boundary conditions preserving (2,2) and (0,4) supersymmetry in 3d N=4 theories, including their BPS equations and brane realizations.

Findings

Derivation of BPS equations for boundary conditions.

Identification of Nahm-like equations in (0,4) case.

Realization of boundary conditions via Type IIB branes.

Abstract

The half-BPS boundary conditions preserving $\mathcal{N}=(2,2)$ and $\mathcal{N}=(0,4)$ supersymmetry in 3d $\mathcal{N}=4$ supersymmetric gauge theories are examined. The BPS equations admit decomposition of the bulk supermultiplets into specific boundary supermultiplets of preserved supersymmetry. Nahm-like equations arise in the vector multiplet BPS boundary condition preserving $\mathcal{N}=(0,4)$ supersymmetry and Robin-type boundary conditions appear for the hypermultiplet coupled to vector multiplet when $\mathcal{N}=(2,2)$ supersymmetry is preserved. The half-BPS boundary conditions are realized in the brane configurations of Type IIB string theory.