Quantum Annihilation of Anti-de Sitter Universe

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 quantum maximally supersymmetric Yang-Mills theory covariantly coupled with classical N = 4 conformal supergravity is considered as a typical example of conformal GUT. 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. 1. There is a large interest now in studies related to Anti-de Sitter (AdS) backgrounds. This is caused by several reasons. First of all, via the AdS/CFT correspondence (for a review,see [1]) investigating the classical IIB supergravity on an AdS background (after compactification), one can get answers for the dual (boundary) quantum gauge theory. Second, the AdS space is extremely symmetric one (maximum number of Killing vectors), like Minkowski space. Moreover, it is a well-known supersymmetric background for supergravity theories. For strings the backgrounds with AdS section are often suspected to be the exact vacuum state. Third, according to some cosmological data the inflationary Universe could have the spatial section with negative curvature. Generalizing this for a brane world one can speculate on the possibility of 4d AdS stage (or regions) in the early Universe. The important question is: how should one create the AdS regions in the early Universe? The mechanisms of such creation maybe important for the realization of AdS Black Holes presence. In this note we investigate the role of matter quantum effects to the Anti-de Sitter Universe. It is well known that the inflationary (de Sitter) Universe maybe created completely by quantum effects of conformally invariant matter. On the contrary, as we will show below, the quantum creation of Anti-de Sitter Universe by quantum effects is rather unrealistic. The quantum annihilation of such a Universe occurs. Only in presence of dilaton the fine-tuning of the dilaton solution may lead to quantum creation of the AdS Universe (an example of quantum maximally supersymmetric YM theory conformally coupled to conformal background supergravity).