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Gauge Field Emergence from Kalb-Ramond Localization

A new mechanism, valid for any smooth version of the Randall-Sundrum model, of getting localized massless vector field on the brane is described here. This is obtained by dimensional reduction of a five dimension massive two form, or Kalb-Ramond field, giving a Kalb-Ramond and an emergent vector field in four dimensions. A geometrical coupling with the Ricci scalar is proposed and the coupling constant is fixed such that the components of the fields are localized. The solution is obtained by decomposing the fields in transversal and longitudinal parts and showing that this give decoupled equations of motion for the transverse vector and KR fields in four dimensions. We also prove some identities satisfied by the transverse components of the fields. With this is possible to fix the coupling constant in a way that a localized zero mode for both components on the brane is obtained. Then, all the above results are generalized to the massive $p-$form field. It is also shown that in general an effective $p$ and $(p-1)-$forms can not be localized on the brane and we have to sort one of them to localize. Therefore, we can not have a vector and a scalar field localized by dimensional reduction of the five dimensional vector field. In fact we find the expression $p=(d-1)/2$ which determines what forms will give rise to both fields localized. For $D=5$, as expected, this is valid only for the KR field.