Two-dimensional black holes in a higher derivative gravity and matrix model

We construct perturbatively a class of charged black hole solutions in type 0A string theory with higher derivative terms. They have extremal limit, where the solution interpolates smoothly between near horizon AdS2 geometry and the asymptotic linear dilaton geometry. We compute the free energy and the entropy of those solutions using various methods. In particular, we show that there is no correction in the leading term of the free energy in the large charge limit. This supports the duality of the type 0A strings on the extremal black hole and the 0A matrix model in which the tree level free energy is exact without any α′ corrections in the leading order.