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. Also, 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 stringlike 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 height of the barrier around the brane. The massive modes are slightly changed near the brane but they agree with the stringlike spectrum for large distances.

In this work we investigate the properties of an Abelian gauge vector field in a thin and in a smoothed string-like braneworld, the so-called string-cigar model. This thick brane scenario satisfies the regularity conditions and it can be regarded as an interior and exterior string-like solution. The source undergoes a geometric Ricci flow which is connected to a variation of the bulk cosmological constant. The Ricci flow changes the width and amplitude of the massless mode at the brane core and recover the usual thin string-like behavior at large distances. By numerical means we obtain the Kaluza-Klein (KK) spectrum for both the thin brane and the string-cigar. It turns out that both models exhibit a mass gap between the massless and the massive modes and between the high and the low mass regimes. The KK modes are smooth near the brane and their amplitude are enhanced by the string-cigar core. The analogue Schr\"odinger potential is also tuned by the geometric flow.Comment: The discussion about the Kaluza-Klein spectrum of the gauge field was improved. Numerical analysis was adapted to the conventional notation on Kaluza-Klein number. Some graphics were modified for considering other notation. Results unchanged. References added. Corrected typos. 17 pages. 6 figures. To match version to appears in Physics Letters

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