  The hybrid formalism is used to quantize the superstring compactified to
two-dimensional target-space in a manifestly spacetime supersymmetric manner. A
quantizable sigma model action is then constructed for the Type II superstring
in curved two-dimensional supergravity backgrounds which can include
Ramond-Ramond flux. Such curved backgrounds include Calabi-Yau four-fold
compactifications with Ramond-Ramond flux, and new extremal black hole
solutions in two-dimensional dilaton supergravity theory. These black hole
solutions are a natural generalization of the CGHS model and might be possible
to describe using a supergroup version of the SL(2,R)/U(1) WZW model. We also
study some dynamical aspects of the new black holes, such as formation and
evaporation.
