Concentrating Gravity on Branes

There is a taxonomy of different kinds of lower-dimensional effective field theory on brane configurations, depending on the boundary conditions imposed near the brane worldvolume. Branes with a certain degree of unbroken supersymmetry can embody consistent Kaluza-Klein truncations to braneworld supergravity theories with that degree of supersymmetry, and arbitrarily nonlinear solutions of such lower-dimensional braneworld supergravities can be found. This applies only to solutions purely within that pure supergravity, however — external sources give rise to responses in structure characteristic of the higher dimensional theory. There exists another taxonomic type, however, in which a genuine concentration of gravity can occur for more general sources, depending on details of the wave equation for modes transverse to the brane worldvolume, implemented by a set of boundary conditions different from the standard Kaluza-Klein ones. Such a genuine concentration does not correspond to a KK consistent truncation, but does give rise to an effective lower-dimensional gravitational theory – revealed, for example, in a transition from higher-dimensional near-field behaviour to lower-dimensional far-field behaviour.