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

We have studied the localization of a scalar field on a 3-brane embedded in a six-dimensional warped bulk of the form M-4 X C-2, where M-4 is a 3-brane and C-2 is a 2-cycle of a six-dimensional resolved conifold C-6 over a T-1,T-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 a scalar field when we vary the resolution parameter. On one hand, this enables 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 not equal 0). We have also compared the results obtained in this geometry and those obtained in other six-dimensional models, such as stringlike geometry and cigarlike universe geometry.