  We discuss the role of conformal matter quantum effects (using large $N$
anomaly induced effective action) to creation-annihilation of an Anti-de Sitter
Universe. The arbitrary GUT with conformally invariant content of fields is
considered. On a purely gravitational (supersymmetric) AdS background, the
quantum effects act against an (already existing) AdS Universe. The
annihilation of such a Universe occurs, what is common for any conformal matter
theory. On a dilaton-gravitational background, where there is dilatonic
contribution to the induced effective action, the quantum creation of an AdS
Universe is possible assuming fine-tuning of the dilaton.
