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

TL;DR

This paper proposes a scenario where quantum fluctuations of a D3 brane generate a mass hierarchy, leading to a discrete KK spectrum with localized modes, potentially addressing the gauge hierarchy problem.

Contribution

It introduces a novel mechanism linking D3 brane quantum fluctuations to mass hierarchies and discrete spectra, with implications for supersymmetry breaking and localization.

Findings

Discrete mass spectrum for KK modes of bulk fields.

Localized wavefunctions of low-mass KK modes on the brane.

Bulk string scale naturally at 10^{14} GeV.

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 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 < sqrt{2}alpha << M_s are found to have wavefunctions peaked, and hence localized, on the D3 brane at z=0.