Kink modes and effective four dimensional fermion and Higgs brane models

Abstract In the construction of a classical smoothed out brane world model in five dimensions, one uses a dynamically generated domain wall (a kink) to localise an effective four dimensional theory. At the level of the Euler-Lagrange equations, the kink sets up a potential well which can trap certain suitably coupled fields. This mechanism has been employed extensively to obtain localised, four dimensional, massless chiral fermions; these are crucial ingredients from the model building point of view. We present the generalisation of this kink trapping mechanism for both scalar and fermionic fields, and retain all degrees of freedom that were present in the higher dimensional theory. We show that a kink background induces a symmetric modified Pöschl-Teller potential well, and give explicit analytic forms for all the bound modes and a restricted set of the continuum modes. We demonstrate that it is possible to confine an effective four dimensional scalar field with a quartic potential of arbitrary shape. This can be used to place the standard model electroweak Higgs field on the brane, and also generate nested kink solutions. We also consider the limits of the parameters in the theory which give thin kinks and localised and de-localised scalar and fermionic fields.