Domain walls inside localised orientifolds

The equations of motion of toroidal orientifold compactifications with fluxes are in one-to-one correspondence with gauged supergravity if the orientifold (and D-brane) sources are smeared over the compact space. This smeared limit is identical to the approximation that ignores warping. It is therefore relevant to compare quantities obtained from the gauged supergravity with the true 10d solution with localised sources. In this paper we find the correspondence between BPS domain walls in gauged SUGRA and 10D SUGRA with localised sources. Our model is the simplest orientifold with fluxes we are aware of: an O6/D6 compactification on T³/ℤ₂ in massive IIA with H₃-flux. The BPS domain walls correspond to a O6/D6/NS5/D8 bound state. Our analysis reveals that the domain wall energy computed in gauged SUGRA is unaffected by the localisation of the O6/D6 sources.