2D anti–de Sitter gravity as a conformally invariant mechanical system

We show that two-dimensional (2D) AdS gravity induces on the spacetime boundary a conformally invariant dynamics that can be described in terms of a de Alfaro–Fubini–Furlan model coupled to an external source with conformal dimension 2. The external source encodes information about the gauge symmetries of the 2D gravity system. Alternatively, there exists a description in terms of a mechanical system with anholonomic constraints. The considered systems are invariant under the action of the conformal group generated by a Virasoro algebra, which occurs also as an asymptotic symmetry algebra of two-dimensional anti–de Sitter space. We calculate the central charge of the algebra and find perfect agreement between the statistical and thermodynamical entropies of ${\mathrm{AdS}}_2$ black holes.