SO/Sp monopoles and branes with an orientifold 3-plane

We study BPS monopoles in four-dimensional $N=4$ $\mathrm{SO}(N)$ and $\mathrm{Sp}(N)$ super-Yang-Mills theories realized as the low-energy effective theory of $N$ (physical and its mirror) parallel D3-branes and an orientifold 3-plane with D1-branes stretched between them in type-IIB string theory. Monopoles on D3-branes give a natural understanding by embedding in $\mathrm{SU}(N)$ through the constraints on both the asymptotic Higgs field (corresponding to the horizontal positions of D3-branes) and the magnetic charges (corresponding to the number of D1-branes) imposed by the O3-plane. The compatibility conditions of Nahm data for monopoles for these groups can be interpreted very naturally through the D1-branes in the presence of the O3-plane.