We elaborate further on a recently proposed scenario for generating a mass hierarchy through quantum fluctuations of a single D3-brane, which represents our world embedded in a bulk five-dimensional space-time. In this scenario, the quantum fluctuations of the D3-brane world in the bulk direction, quantified to leading order via a “recoil” world-sheet logarithmic conformal field theory approach, result in the dynamical appearance of a supersymmetry breaking (obstruction) scale $\alpha .$ This may be naturally taken to be at the TeV range, in order to provide a solution to the conventional gauge-hierarchy problem. The bulk spatial direction is characterized by the dynamical appearance of a horizon located at $\pm 1/\alpha ,$ inside which the positive energy conditions for the existence of stable matter are satisfied. To ensure the correct value of the four-dimensional Planck mass, the bulk string scale $M_s$ is naturally found to lie at an intermediate energy scale of ${10}^{14}\hspace{0.5em}\mathrm{GeV}.$ As an exclusive feature of the D3-brane quantum fluctuations (“recoil”) we find that, for any given $M_5,$ there is a discrete mass spectrum for four-dimensional Kaluza-Klein (KK) modes of bulk graviton and/or scalar fields. KK modes with masses $0<~m<\mathrm{}\sqrt{2}\alpha \ll M_s$ are found to have wave functions peaked, and hence localized, on the D3-brane at $z=0.\mathrm{}$

• Received 14 November 2000

DOI:https://doi.org/10.1103/PhysRevD.64.024008