Extending cascading gravity model to lower dimensions

The cascading gravity model was proposed to eliminate instabilities of the original DGP model by embedding our 4D universe into a 5D brane, which is itself embedded in a 6D bulk. Thus gravity cascades from 6D down to 4D as we decrease the length scales. We show that it is possible to extend this setup to lower dimensions as well, i.e. there is a self-consistent embedding of a 3D brane into a 4D brane, which is itself embedded in a 5D bulk and so on. This extension fits well into the "vanishing dimensions" framework in which dimensions open up as we increase the length scales.