Consistency of Higher Derivative Gravity in the Brane Background

Abstract

We consider the theory of higher derivative gravity with non-factorizable Randall-Sundrum type space-time and obtain the metric solutions which characterize the $p$-brane world-volume as a curved or planar defect embedded in the higher dimensions. We consider the string inspired effective actions of the dilatonic Gauss-Bonnet type in the brane background and show its consistency with the RS brane-world scenario and the conformal weight of the dilaton couplings in the string theory with apppropriate choice of Regge slope (${\alpha }^{\prime }$) or Gauss-Bonnet coupling ($\alpha$) or both. We also discuss a time dependent dilaton solution for a string-inspired fourth-derivative gravity.

20 pages, LaTex, V2 notational differences corrected, V3 typos corrected and references added, V4 the version in JHEP 0009 (2000) 040

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