Orbifold ETW brane and half-indices

We study the half-indices of $\mathcal{N}=4$ super Yang-Mills theories of orthogonal and symplectic gauge groups. We find precise matching pairs of the half-indices as strong evidence of dualities of the half-BPS boundary conditions and interfaces. The half-indices encode the spectra of excitations on the holographically dual orbifold ETW brane and giant gravitons. The exact form of the index for the orbifold ETW giant gravitons is obtained from the giant graviton expansion of the half-index.