POSITIVE-ENERGY THEOREM AND SUPERSYMMETRY IN EXACTLY SOLVABLE QUANTUM-CORRECTED 2-DIMENSIONAL DILATON GRAVITY

Extending the work of Park and Strominger, we prove a positive-energy theorem for the exactly solvable quantum-corrected two-dimensional 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 linear dilaton vacuum we show that this energy functional (if defined on a spacelike surface) yields the usual (classical) definition of the Arnowitt-Deser-Misner (ADM) mass plus a certain ''quantum'' correction. If defined on a null surface the energy functional yields the Bondi mass. The latter is evaluated carefully and applied to the Russo-Susskind-Thorlacius (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.