Scalar field localization on 3-branes placed at a warped resolved conifold

TL;DR

This paper investigates how scalar fields can be localized on a 3-brane within a six-dimensional warped space modeled by a resolved conifold, analyzing the effects of the conifold's resolution parameter on field trapping and hierarchy problem implications.

Contribution

It introduces a new analysis of scalar field localization on a 3-brane in a resolved conifold geometry, highlighting the role of the resolution parameter in field trapping and hierarchy tuning.

Findings

Scalar fields are localized on the brane even with a singular cone.

The resolution parameter affects the localization behavior and hierarchy relation.

Comparison with other six-dimensional models shows similar trapping phenomena.

Abstract

We have studied the localization of scalar field on a 3-brane embedded in a six dimensional warped bulk of the form $M_{4}\times C_{2}$, where $M_{4}$ is a 3-brane and $C_{2}$ is a 2-cycle of a six resolved conifold $\mathcal{C}_{6}$ over a $T^{1,1}$ space. Since the resolved conifold is singularity-free in $r=0$ depending on a resolution parameter $a$, we have analyzed the behavior of the localization of scalar field when we vary the resolution parameter. On one hand, this enable us to study the effects that a singularity has on the field. On the other hand we can use the resolution parameter as a fine-tuning between the bulk Planck mass and 3-brane Planck mass and so it opens a new perspective to extend the hierarchy problem. Using a linear and a nonlinear warp factor, we have found that the massive and massless modes are trapped to the brane even in the singular cone ($a\neq 0$). We have also compared the results obtained in this geometry and those obtained in other six-dimensional models, as string-like geometry and cigar-like universe geometry.