Mitchell Institute for Fundamental Physics & Astronomy
College Station, Texas 77843
There is a taxonomy of effective theory types on or near branes in supergravity. One type constitutes consistent embeddings of lower-dimensional supergravities on the worldvolumes, but another leads to a specific concentration of gravity near the worldvolume. The difference lies in the boundary conditions imposed on fluctuation spectra about the brane background. An analysis originating from Hermann Weyl for singular Sturm-Liouville systems helps to classify the possibilities for gravity concentration, using the notions of limit circles and limit points.