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, by analysing their low energy equations of motion at leading order in alpha ' . 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 AdS2 form, there is a need for an exact worldsheet description. We discuss relevant WZW coset models which 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.