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Gauge vector field localization on 3-brane placed in a warped transverse resolved conifold

We have investigated the features of the gauge vector field in a braneworld scenario built as a warped product between a 3-brane and a 2-cycle of the resolved conifold. This scenario allowed us to study how the gauge field behaves when the transverse manifold evolves upon a geometric flow that controls the singularity at the origin. Besides, since the transverse manifold has a cylindrical symmetry according to the 3-brane, this geometry can be regarded as a near brane correction of the string-like branes. Indeed, by means of a new warp function and the angular metric component of the resolved conifold, the braneworld can exhibit a conical form near the origin as well as a regular behavior in that region. The analysis of the gauge field in this background has been carried out for the s-wave state and a normalizable massless mode was found. For the massive modes, the resolution parameter avoids an infinite well on the brane and controls the depth of the well and the high of the barrier around the brane. The massive modes are slightly changed near the brane but they agreed with the string-like spectrum for large distances.