TRACE ANOMALY INDUCED EFFECTIVE ACTION AND 2D BLACK-HOLES FOR DILATONCOUPLED SUPERSYMMETRIC THEORIES

The action for two-dimensional (2D) dilatonic supergravity with dilato n coupled matter and dilaton multiplets is constructed. A trace anomal y and anomaly induced effective action (in components as well as in su persymmetric form) for a matter supermultiplet on a bosonic background are found. The one-loop effective action and large-N effective action for quantum dilatonic supergravity an also calculated. Using an induc ed effective action one can estimate the back reaction of dilaton coup led matter to the classical black hole solutions of dilatonic supergra vity. That is done on the example of a supersymmetric CGHS model with dilaton coupled quantum matter where Hawking radiation which turns out to be zero is calculated. A similar 2D analysis may be used to study spherically symmetric collapse for other models of 4D supergravity.