Antisymmetric tensor fields in Randall-Sundrum thick branes

In this Letter 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 alpha = -1.75 and alpha = -20. The first value of alpha give us one resonance peak for p = 1 and no resonances for p = 3, 5. The second value of alpha give us a very rich structure of resonances, with number depending on the value of p. (C) 2010 Elsevier B.V. All rights reserved.