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

The action for 2d dilatonic supergravity with dilaton coupled matter and dilaton multiplets is constructed. Trace anomaly and anomaly induced effective action (in components as well as in supersymmetric form) for matter supermultiplet on bosonic background are found. The one-loop effective action and large-$N$ effective action for quantum dilatonic supergravity are also calculated. Using 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 supersymmetric CGHS model with dilaton coupled quantum matter where Hawking radiation which turns out to be zero is calculated. Similar 2d analysis maybe used to study spherically symmetric collapse for other models of 4d supergravity.Comment: 21 pages, LaTeX, NDA-FP-3

Quantum cosmology in the models of 2d and 4d dilatonic supergravity with WZ matter

We consider N=1 two-dimensional (2d) dilatonic supergravity (SG), 2d dilatonic SG obtained by dimensional reduction from N=1 four-dimensional (4d) SG, N=2 2d dilatonic SG and string-inspired 4d dilatonic SG. For all the theories, the corresponding action on a bosonic background is constructed and the interaction with $N$ (dilatonic) Wess-Zumino (WZ) multiplets is presented. Working in the large-N approximation, it is enough to consider the trace anomaly induced effective action due to dilaton-coupled conformal matter as a quantum correction (for 2d models s-waves approximation is additionally used). The equations of motion for all such models with quantum corrections are written in a form convenient for numerical analysis. Their solutions are numerically investigated for 2d and 4d Friedmann-Robertson-Walker (FRW) or 4d Kantowski-Sacks Universes with a time-dependent dilaton via exponential dilaton coupling. The evolution of the corresponding quantum cosmological models is given for different choices of initial conditions and theory parameters. In most cases we find quantum singular Universes. Nevertheless, there are examples of Universe non-singular at early times. Hence, it looks unlikely that quantum matter back reaction on dilatonic background (at least in large $N$ approximation) may really help to solve the singularity problem.Comment: LaTeX file of the text (36 pages) and 3 ps files of 14 figures, few misprints are corrected and references adde