Consistency Conditions for Fields Localization on Braneworlds

Abstract

The general procedure for analyzing the localization of matter fields in Brane models is by integrating, in the action, its zero mode solutions over the extra dimensions. If this is finite, the field is said to be localized. However, the zero mode solutions must also satisfy the Einstein equations. With this in mind, we obtain stringent constraints on a general energy-momentum tensor by analyzing the Einstein's equations. These {\it consistency conditions} must be satisfied for any Braneworld model. We apply it for some fields of the Standard Model. For a free massless scalar field, the zero-mode localization is consistent only if the field does not depend on the extra dimensions. About the spin $\frac{1}{2}$ field with Yukawa-like interactions, we find a very specific relation between Yukawa function and the warp factor. As a consequence, the spinor field localization becomes inconsistent for most of the models studied in the literature. For the free vector field case we find that, independent of the braneworld or the number of extra dimensions, the zero-mode do not satisfy the consistency conditions. Finally, we consider the mechanisms proposed to localize this field. We find that a few survive, and even for these, the consistency conditions fix the free parameters or the possible class of solutions allowed.