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We investigate the vacuum expectation value of the surface energy-momentumtensor for a massive scalar field with general curvature coupling parameterobeying the Robin boundary conditions on two codimension one parallel branes ina (D+1)-dimensional background spacetime $AdS_{D_{1}+1}\times \Sigma $ with awarped internal space $\Sigma $. These vacuum densities correspond to agravitational source of the cosmological constant type for both subspaces ofthe branes. Using the generalized zeta function technique in combination withcontour integral representations, the surface energies on the branes arepresented in the form of the sum of single brane and second brane inducedparts. For the geometry of a single brane both regions, on the left and on theright of the brane, are considered. At the physical point the correspondingzeta functions contain pole and finite contributions. For an infinitely thinbrane taking these regions together, in odd spatial dimensions the pole partscancel and the total zeta function is finite. The renormalization procedure forthe surface energies and the structure of the corresponding counterterms arediscussed. The parts in the surface densities generated by the presence of thesecond brane are finite for all nonzero values of the interbrane separation andare investigated in various asymptotic regions of the parameters. Inparticular, it is shown that for large distances between the branes the inducedsurface densities give rise to an exponentially suppressed cosmologicalconstant on the brane. The total energy of the vacuum including the bulk andboundary contributions is evaluated by the zeta function technique and theenergy balance between separate parts is discussed.Comment: 21 pages, 5 figures, REVTeX, references adde

Surface Casimir densities and induced cosmological constant in higher dimensional braneworlds