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Antisymmetric Tensor Fields in Randall Sundrum Thick Branes

In this article we study the issue of localization of the three-form field in a Randall-Sundrum-like scenario. We simulate our membrane by kinks embedded in D=5, describing the usual case (not deformed) and new models coming from a specific deformation procedure. The gravitational background regarded includes the dilaton contribution. We show that we can only localize the zero-mode of this field for a specific range of the dilaton coupling, even in the deformed case. A study about resonances is presented. We use a numerical approach for calculations of the transmission coefficients associated to the quantum mechanical problem. This gives a clear description of the physics involved in the model. We find in this way that the appearance of resonances is strongly dependent on the coupling constant. We study the cases $p=1,3$ and 5 for $α=-1.75$ and $α=-20$. The first value of $α$ give us one resonance peak for $p=1$ and no resonances for $p=3,5$. The second value of $α$ give us a very rich structure of resonances, with number deppending on the value of $p$.