Positive Energy Theorem and Supersymmetry in Exactly Solvable Quantum-Corrected 2D Dilaton-Gravity

Extending the work of Park and Strominger, we prove a positive energy theorem for the exactly solvable quantum-corrected 2D dilaton gravity theories. The positive energy functional we construct is shown to be unique (within a reasonably broad class of such functionals). For field configurations asymptotic to the LDV we show that this energy functional (if defined on a space-like surface) yields the usual (classical) definition of the ADM mass {\it plus a certain ``quantum"-correction. If defined on a null surface the energy functional yields the Bondi mass. The latter is evaluated careflly and applied to the RST shock-wave scenario where it is shown to behave as physically expected. Motivated by the existence of a positivity theorem we construct manifestly supersymmetric (semiclassical) extensions of these quantum-corrected dilaton-gravity theories.