A Novel Mass Hierarchy and Discrete Excitation Spectra from Quantum-fluctuating D-branes

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 α. 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 an horizon located at ±1/α, 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 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 < √ 2α << M s are found to have wavefunctions peaked, and hence localized, on the D3 brane at z = 0.