Self-tuning flat domain walls in 5D gravity and string theory

We present Poincaré-invariant domain wall (“three-brane”) solutions to some five-dimensional effective theories which can arise naturally in string theory. In particular, we find theories where Poincaré-invariant solutions exist for arbitrary values of the brane tension, for certain restricted forms of the bulk interactions. We describe examples in string theory where it would be natural for the quantum corrections to the tension of the brane (arising from quantum fluctuations of modes with support on the brane) to maintain the required form of the action. In such cases, the Poincaré-invariant solutions persist in the presence of these quantum corrections to the brane tension, so that no 4D cosmological constant is generated by these modes.