with the induced metric $h_{ab}$. All integrations over the bulk and brane are taken with the natural volume elements $\sqrt{-g}d^{5}x$ and $\sqrt{-h}d^4x$, respectively, where $g$ and $h$ are the determinants of the matrices of components of the corresponding metrics in a coordinate basis. The symbols $M$ and $m$ denote, respectively, the five- and four-dimensional Planck masses, $\Lambda_{\rm b}$ is the bulk cosmological constant, and $\sigma$ is the brane tension.

The term containing the scalar curvature of the induced metric on the brane with the coupling $m^2$ in action (\[act\]) was originally absent from braneworld models. However, very soon it became clear that this term is qualitatively essential for describing the braneworld dynamics and, moreover, it is inevitably generated as a quantum correction to the matter action in (\[act\]) — in the spirit of an idea that goes back to Sakharov [@Sakharov] (see also [@BD]). Note that the effective action for the brane typically involves an infinite number of terms of higher order in curvature (this was pointed out in [@CHS] for the case of braneworld theory; a similar situation in the context of the AdS/CFT correspondence is described in [@HHR]). In this paper, we retain only the terms linear in 