Higher derivative gravity in two dimensions

The two-dimensional (2D) gravity described by the action which is an arbitrary function of the scalar curvature f(R) is considered. The classical vacuum solutions are analyzed. The one-loop renormalizability is studied. For the function f=R lnR the model coupled with scalar (conformal) matter is exactly integrated and is shown to describe a black hole of the 2D dilaton gravity type. The influence of one-loop quantum corrections on a classical black hole configuration is studied by including the Liouville-Polyakov term. The resulting model turns out to be exactly solvable. The general solution is analyzed and shown to be free from the space-time singularities for a certain number of scalar fields.