Graviton KK resonant mode in the correction of the Newton's law from 6D braneworlds

TL;DR

This paper derives the correction to Newton's law from gravitational Kaluza-Klein states in a 6D braneworld model, analyzing the spectrum and resonant modes that influence gravitational behavior at small scales.

Contribution

It introduces a general thick string-like 6D braneworld model with a resolution parameter, analyzing its spectrum and identifying a resonant mode affecting Newtonian corrections.

Findings

Resonant mode significantly contributes to Newtonian correction.

Resolution parameter influences the physical acceptability of states.

Massless mode recovers 4D gravity and shifts with brane energy density.

Abstract

In this work, we derive an expression for the correction in the Newton's law of gravitation due to the gravitational Kaluza-Klein states in a general thick string-like braneworld scenario in six dimensions. In order to analyze corrections to Newton's law we study the gravity fluctuations in a 3-brane placed in a transverse resolved conifold and use suitable numerical methods to attain the massive spectrum and the corresponding eigenfunctions. Such braneworld model has a resolution parameter which removes the conical singularity. The correction has an exponentially suppressed mass term and depends on the values of the eigenfunctions and warp factors computed at the core peak of the brane. The spectrum is real and monotonically increased, as desired. However, the resolution parameter must assume moderate values to have physically acceptable states. Moreover, the trapped massless mode regains the 4D gravity and it is displaced from the origin, sharing similar profile with the energy density of brane for small values of resolution parameter. Finally, for the singular conifold, we found that a non-first eigenstate is a resonant mode. Such excited state is the largest contributor to corrections in the Newtonian potential.