A Novel Mass Hierarchy and Discrete Excitation Spectra from Quantum-Fluctuating D-branes
Abstract
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 an horizon located at +- 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 Ms is naturally found to lie at an intermediate energy scale of 1014 GeV. As an exclusive feature of the D3-brane quantum fluctuations (`recoil') we find that, for any given M5, 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 < sqrt2alpha << Ms are found to have wavefunctions peaked, and hence localized, on the D3 brane at z=0.
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