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 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 depending on the value of p.