Classification of 5-Dimensional Space-Time with Parallel 3-Branes

TL;DR

This paper classifies 5-dimensional space-times with parallel 3-branes, explores cosmological constants, and demonstrates how these models can address the gauge hierarchy problem.

Contribution

It constructs general models of 5D space-times with parallel 3-branes and constant or sectional constant cosmological constants, analyzing tension conditions and hierarchy problem solutions.

Findings

Sum of brane tensions is zero for compact fifth dimension.

Sum of brane tensions is positive for non-compact fifth dimension.

Observable brane with positive tension can solve the gauge hierarchy problem.

Abstract

If the fifth dimension is one-dimensional connected manifold, up to diffeomorphic, the only possible space-time will be $M^4 \times R^1$, $M^4 \times R^1/Z_2$, $M^4 \times S^1$ and $M^4 \times S^1/Z_2$. And there exist two possibilities on cosmology constant along the fifth dimension: the cosmology constant is constant, and the cosmology constant is sectional constant. We construct the general models with parallel 3-branes and with constant/sectional constant cosmology constant along the fifth dimension on those kinds of the space-time, and point out that for compact fifth dimension, the sum of the brane tensions is zero, for non-compact fifth dimension, the sum of the brane tensions is positive. 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.