Four-dimensional description of five-dimensional $N$-brane models

We propose a new method for obtaining the four-dimensional effective gravitational theory for five-dimensional braneworld models with arbitrary numbers of branes in a low-energy regime, based on a two-length-scale expansion. The method is straightforward and computationally efficient, and is applicable to both compactified and uncompactified models. Particular emphasis is placed on the behavior of the radion modes of the model, while the massive effective fields are automatically truncated. Generally, the radion modes are found to form an ($N-1$)-dimensional nonlinear sigma model. We illustrate the method for a $N$-brane model in an uncompactified extra dimension.

Figure 1

An illustration of the model (a) before and (b) after gauge fixing. The bulk cosmological constants, brane tensions, and metrics are labeled.