(2,2) and (0,4) supersymmetric boundary conditions in 3d N=4 theories and type IIB branes

The half-BPS boundary conditions preserving N = (2,2) and N = (0,4) supersymmetry in 3d 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 N = (0,4) supersymmetry, and Robin-type boundary conditions appear for the hypermultiplet coupled to the vector multiplet when N = (2,2) supersymmetry is preserved. The half-BPS boundary conditions are realized in the brane configurations of type IIB string theory.