String-inspired higher-curvature terms and the Randall-Sundrum scenario

We consider the O(a') string effective action, with Gauss-Bonnetcurvature-squared and fourth-order dilaton-derivative terms, which is derivedby a matching procedure with string amplitudes in five space-time dimensions.We show that a non-factorizable metric of the Randall-Sundrum (RS) type, withfour-dimensional conformal factor Exp(-2 k|z|), can be a solution of thepertinent equations of motion. The parameter k is found proportional to thestring coupling g_s and thus the solution appears to be non-perturbative. It iscrucial that the Gauss-Bonnet combination has the right (positive in ourconventions) sign, relative to the Einstein term, which is the casenecessitated by compatibility with string (tree) amplitude computations. Westudy the general solution for the dilaton and metric functions, and thusconstruct the appropriate phase-space diagram in the solution space. In thecase of an anti-de-Sitter bulk, we demonstrate that there exists a continuousinterpolation between (part of) the RS solution at z=infinity and an(integrable) naked singularity at z=0. This implies the dynamical formation ofdomain walls (separated by an infinite distance), thus restricting the physicalbulk space time to the positive z axis. Some brief comments on the possibilityof fine-tuning the four-dimensional cosmological constant to zero are alsopresented.Comment: 28 pages Latex, three eps figures incorporated, minor change