Classification of 5-dimensional space–time with parallel 3-branes

Abstract

If the fifth dimension is a one-dimensional connected manifold, up to diffeomorphism, the only possible space–times will be M 4 × R 1 , M 4 × R 1 / Z 2 , M 4 × S 1 and M 4 × S 1 / Z 2 . And there exist two possibilities for the cosmological constant along the fifth dimension: the cosmological constant is constant, and the cosmological constant is sectionally constant. We construct general models with parallel 3-branes and constant/sectionally constant cosmological constant along the fifth dimension on those kinds of the space–times. Moreover, we point out that for a compact fifth dimension, the sum of the brane tensions is zero, and for a non-compact fifth dimension, the sum of the brane tensions is positive. Furthermore, we assume the observable brane which includes our world should have positive tension, and obtain that the gauge hierarchy problem can be solved in those scenarios. We also discuss some simple models.