Novel mass hierarchy and discrete excitation spectra from quantum-fluctuating D-branes - art. no. 024008

We elaborate further on a recently proposed scenario for generating a mass hierarchy through quantum fluctuations of a single D3-brane, which represen ts our world embedded in a bulk five-dimensional space-time. In this scenar io, the quantum fluctuations of the D3-brane world in the bulk direction, q uantified to leading order via a "recoil" world-sheet lograrithmic conforma l field theory approach, result in the dynamical appearance of a supersymme try breaking (obstruction) scale alpha. This may be naturally taken to be a t the TeV range, in order to provide a solution to the conventional gauge-h ierarchy problem. The bulk spatial direction is characterized by the dynami cal appearance of a horizon located at +/- 1/alpha, inside which the positi ve energy conditions for the existence of stable matter are satisfied. To e nsure the correct value of the four-dimensional Planck mass, the bulk strin g 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 ("re coil") we iind that, for any given M-5, there is a discrete mass spectrum f or four-dimensional Kaluza-Klein (KK) modes of bulk graviton and/or scalar fields. KK modes with masses 0 less than or equal tom<<root>2 alpha<<M-s ar e found to have wave functions peaked, and hence localized, on the D3-brane at z=0.