Alex will give a journal club talk on 10/31/2018. The title is “Classification and characterization of higher-order SPT phases” which is a recent paper by Alex and Yuan-Ming https://arxiv.org/abs/1809.07325.
I think the idea here is to find protected states on the edge of an edge. A hallmark of SPT phases is interesting edge modes, e.g., on the surface of a d-dimensional theory there is an interesting d-1-dimensional object. What about d-2-dimensional objects?
I asked Alex and this is not quite the right idea. The notion of confinement to a lower dimensions, e.g., 2D->1D->0D is not as important as the idea of symmetry. Where the boundary modes exist are related by symmetry.