Black hole - wormhole transitions in two dimensional string theory

We study charged black hole and wormhole solutions of Type 0A/IIA string theory in two dimensions. There is a competition between Euclidean wormholes and near extremal black holes in the thermodynamic ensemble. In a certain regime of phase space, the former can disassociate into the latter. Since such solutions are of string scale near the wormhole throat that takes an $AdS_2$ form, there is a need for an exact worldsheet description. We discuss relevant WZW coset models which we we argue will shed light on this problem. Finally, we present appropriate versions of the Type 0A/IIA matrix quantum mechanics models that are expected to describe these geometries.