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We show that a scalar field conformally coupled to AdS gravity in fourdimensions with a quartic self-interaction can be embedded into M-theory. Theholographic effective potential is exactly calculated, allowing us to studynon-perturbatively the stability of AdS_4 in the presence of the conformallycoupled scalar. It is shown that there exists a one-parameter family ofconformal scalar boundary conditions for which the boundary theory has anunstable vacuum. In this case, the bulk theory has instanton solutions thatmediate the decay of the AdS_4 space. These results match nicely with thevacuum structure and the existence of instantons in an effectivethree-dimensional boundary model.

Conformally Coupled Scalars, Instantons, and Vacuum Instability in 4D Anti-de Sitter Space