About fermion hierarchies from doubly warped extra dimensions

Abstract

We consider fermions propagating in the bulk of the geometry found by deforming AdS5 via the back reaction of a scalar field upon the metric. This space is AdS for r asymptotically large (in the UV) but goes through a transition at a point r=r⁎, into another AdS space with different curvature in the IR. Masses are generated for these fermions via electroweak symmetry breaking, by coupling them to a VEV on the IR boundary. We calculate the mass spectrum in four dimensions, comparing approximate results and results found by solving the full system of bulk equations and boundary conditions. We consider the effect on the mass of the light modes of various parameters, including the curvature of the space in the region r<r⁎. This information is then used to reproduce the mass hierarchy between the top and bottom. By assuming universality of the gauge coupling, we find bounds on the allowed bulk masses of the right-handed fermion fields. We look for solutions that satisfy these bounds in a number of different scenarios and find that, for given choices of the other parameters in this model, the IR curvature has a significant influence on whether these bounds can be satisfied or not.