Generalization of Einstein-Lovelock theory to higher order dilaton gravity

A higher order theory of dilaton gravity is constructed as a generalization of the Einstein-Lovelock theory of pure gravity. Its Lagrangian contains terms with higher powers of the Riemann tensor and of the first two derivatives of the dilaton. Nevertheless, the resulting equations of motion are quasi-linear in the second derivatives of the metric and of the dilaton. This property is crucial for the existence of brane solutions in the thin wall limit. At each order in derivatives the contribution to the Lagrangian is unique up to an overall normalization. Relations between symmetries of this theory and the O(d,d) symmetry of the string-inspired models are discussed.