2012-02-25, Lubos, you are a carehctar! Glad you liked the portraits, and yes I am South African!I gave a seminar at MIT about the measure in inflation (maybe you were there?). Alex gave an inflationary measure seminar at Harvard which you blogged about and were a gracious host (I was in the audience).Here are a few thoughts addressing some of your comments:It's really the brane (not a domain wall) that is localized in the extra dimensions. The membrane has co-dimension 3: one co-dimension is in the 4d space and two co-dimensions are in the compactified directions. So indeed, the membrane is only a domain wall from the 4d viewpoint. In the paper we called the instanton which describes the nucleation of the membrane a bubble ring instanton : bubble corresponds to how the instanton looks in 4d and ring corresponds to how the instanton looks in the extra dimensions. As you say, when the instanton is large there is an effective 4d description with domain walls of co-dimension 1. In the paper we considered both limits where the instanton is bigger and much smaller than the size of the compact manifold.When the instanton is much smaller than the size of the compact dimensions, it describes the nucleation of spherical 2-branes in a constant external field in 6d. This is a higher-dimensional analogy for the nucleation of monopole-antimonopole pairs in a homogeneous magnetic field.I think that even with different p-form fluxes we'de expect something similar: the branes that appear in the instanton would be coupled to those forms and should have some energy density that will fall off quickly with the radial distance from the brane.So if the extra dimension is large most of the energy of the brane is concentrated near the brane and we can say it is localized in the extra dimension.