# The hierarchy problem, radion mass, localization of gravity and 4D effective Newtonian potential in string theory on $S^{1}-Z {2}$ - High Energy Physics - Phenomenology

The hierarchy problem, radion mass, localization of gravity and 4D effective Newtonian potential in string theory on $S^{1}-Z {2}$ - High Energy Physics - Phenomenology - Download this document for free, or read online. Document in PDF available to download.

Abstract: We present a systematical study of brane worlds in string theory on$S^{1}-Z {2}$. Starting with the toroidal compactification of the NS-NS sectorin D+d dimensions, we first obtain an effective $D$-dimensional action, andthen compactify one of the $D-1$ spatial dimensions by introducing twoorbifold branes as its boundaries. By combining the Gauss-Codacci and Lanczosequations, we write down explicitly the general gravitational field equationson each of the two branes, while using distribution theory we express thematter field equations on the branes in terms of the discontinuities of thefirst derivatives of the matter fields. Afterwards, we address three importantissues: i the hierarchy problem; ii the radion mass; and iii thelocalization of gravity, the 4-dimensional Newtonian effective potential andthe Yukawa corrections due to the gravitational high-order Kaluza-Klein KKmodes. With a very conservative estimation, we find that the radion mass is ofthe order of $10^{-2} GeV$. The gravity is localized on the visible brane, andthe spectrum of the gravitational KK modes is discrete and can be of the orderof TeV. The corrections to the 4-dimensional Newtonian potential from thehigher order of gravitational KK modes are exponentially suppressed and can besafely neglected in current experiments. In an appendix, we also present asystematical and pedagogical study of the Gauss-Codacci equations and Israel-sjunction conditions across a D-1-dimensional hypersurface, which can beeither spacelike or timelike.

Author: ** Anzhong Wang, N.O. Santos**

Source: https://arxiv.org/