Hidden conformal symmetry in Randall–Sundrum 2 model: Universal fermion localization by torsion

In this manuscript we describe a hidden conformal symmetry of the second Randall–Sundrum model (RS2). We show how this can be used to localize fermions of both chiralities. The conformal symmetry leaves few free dimensionless constants and constrains the allowed interactions. In this formulation the warping of the extra dimension emerges from a partial breaking of the conformal symmetry in five dimensions. The solution of the system can be described in two alternative gauges: by the metric or by the conformon. By considering this as a fundamental symmetry we construct a conformally invariant action for a vector field which provides a massless photon localized over a Minkowski brane. This is obtained by a conformal non-minimal coupling that breaks the gauge symmetry in five dimensions. We further consider a generalization of the model by including conformally invariant torsion. By coupling torsion non-minimally to fermions we obtain a localized zero mode of both chiralities completing the consistence of the model. The inclusion of torsion introduces a fermion quartic interaction that can be used to probe the existence of large extra dimensions and the validity of the model. This seems to point to the fact that conformal symmetry may be more fundamental than gauge symmetry and that this is the missing ingredient for the full consistence of RS scenarios.