Braneworld gravity: influence of the moduli fields

We consider the case of a generic braneworld geometry in the presence of oneor more moduli fields (e.g., the dilaton) that vary throughout the bulkspacetime. Working in an arbitrary conformal frame, using the generalizedjunction conditions of gr-qc/0008008 and the Gauss--Codazzi equations, wederive the effective ``induced'' on-brane gravitational equations. As usual inbraneworld scenarios, these equations do not form a closed system in that thebulk can exchange both information and stress-energy with the braneworld. Wework with an arbitrary number of moduli fields described by an arbitrary sigmamodel, with arbitrary curvature couplings, arbitrary self interactions, andarbitrary dimension for the bulk. (The braneworld is always codimension one.)Among the novelties we encounter are modifications of the on-branestress-energy conservation law, anomalous couplings between on-brane gravityand the trace of the on-brane stress-energy tensor, and additionalpossibilities for modifying the on-brane effective cosmological constant. Afterobtaining the general stress-energy ``conservation'' law and the ``inducedEinstein equations'' we particularize the discussion to two particularlyattractive cases: for a (n-2)-brane in ([n-1]+1) dimensions we discuss both theeffect of (1) generic variable moduli fields in the Einstein frame, and (2) theeffect of a varying dilaton in the string frame.Comment: LaTeX2e, 23 pages, no figures. V2: three references added, some references updated, no physics change