Supergravity-induced interactions on thick branes

The gravity coupling of the symmetric space sigma model is studied in the solvable Lie algebra parametrization. The corresponding Einstein equations are derived and the energy-momentum tensor is calculated. The results are used to derive the dynamical equations of the warped five-dimensional (5D) geometry for localized bulk scalar interactions in the framework of thick brane world models. The Einstein and scalar field equations are derived for flat brane geometry in the context of minimal and non-minimal gravity-bulk scalar couplings.