Brane world sum rules

A set of consistency conditions is derived from Einstein equations for bran e world scenarios with a spatially periodic internal space. In particular, the sum of the total tension of the at branes and the non-negative integral of the gradient energy of the bulk scalars must vanish. This constraint al lows us to make a simple consistency check of several models. We show that the two-brane Randall-Sundrum model satisfies this constraint, but it does not allow a generalization with smooth branes (domain walls), independently of the issue of supersymmetry. The Goldberger-Wise model of brane stabiliz ation has to include the backreaction on the metric and the fine tuning of the cosmological constant to satisfy the constraints. We check that this is achieved in the De Wolfe-Freedman-Gubser-Karch scenario. Our constraints a re automatically satisfied in supersymmetric brane world models.