Conformally Coupled Scalars, Instantons and Vacuum Instability in AdS_4

TL;DR

This paper investigates the stability of AdS_4 space with a conformally coupled scalar field, revealing conditions for vacuum instability and instanton-mediated decay, with exact holographic potential calculations.

Contribution

It embeds a conformally coupled scalar with quartic interaction into M-theory and exactly computes the holographic effective potential to analyze stability.

Findings

Existence of unstable vacua for certain boundary conditions.

Presence of instantons mediating AdS_4 decay.

Exact holographic potential calculation confirms vacuum structure.

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.