Conformally Coupled Scalars, Instantons and Vacuum Instability in AdS_4

TL;DR

It is shown that a scalar field conformally coupled to AdS gravity in four dimensions with a quartic self-interaction can be embedded into M theory, and there exists a one-parameter family of conformal scalar boundary conditions for which the boundary theory has an unstable vacuum.

Abstract

We show that a scalar field conformally coupled to AdS gravity in four dimensions with a quartic self-interaction can be embedded into M-theory. The holographic effective potential is exactly calculated, allowing us to study non-perturbatively the stability of AdS_4 in the presence of the conformally coupled scalar. It is shown that there exists a one-parameter family of conformal scalar boundary conditions for which the boundary theory has an unstable vacuum. In this case, the bulk theory has instanton solutions that mediate the decay of the AdS_4 space. These results match nicely with the vacuum structure and the existence of instantons in an effective three-dimensional boundary model.

Figures (1)

• Figure 1: Plot of the potential (\ref{['eff_potential']}) on $S^3$ for $\alpha<\kappa/\sqrt{6}l$ (long dashes), $\alpha=\kappa/\sqrt{6}l$ (short dashes), and $\alpha>\kappa/\sqrt{6}l$.