On Higher Derivative Gravity in Two Dimensions
Abstract
The 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 R 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.
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