Microscopic entropy of black holes and AdS₂ quantum gravity

Quantum gravity (QG) on two-dimensional anti-de Sitter spacetime (AdS_2) takes always the form of a chiral conformal field theory (CFT). However, the actual content of the CFT, and in particular its central charge, depends on the background values of the dilaton and Maxwell field. We review the main features of AdS_2 QG with linear dilaton and of AdS_2 QG with constant dilaton and Maxwell field. We also show that the 3D charged Banados-Teitelboim-Zanelli black hole interpolates between these two versions of AdS_2 QG. Applications to the computation of the microscopic entropy of black holes are also discussed.