Trace anomaly induced effective action and 2D black holes for dilaton coupled supersymmetric theories

The action for two-dimensional (2D) dilatonic supergravity with dilaton coupled matter and dilaton multiplets is constructed. A trace anomaly and anomaly induced effective action (in components as well as in supersymmetric 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 induced effective action one can estimate the back reaction of dilaton coupled matter to the classical black hole solutions of dilatonic supergravity. 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.