On the stability and spectrum of non-supersymmetric AdS(5) solutions of M-theory compactified on Kahler-Einstein spaces

TL;DR

This paper analyzes the stability of non-supersymmetric AdS(5) solutions in M-theory compactified on Kahler-Einstein spaces, identifying spectral conditions for stability and exploring specific cases like CP(3) and product spaces.

Contribution

It provides a spectral criterion for stability of non-supersymmetric AdS(5) solutions in M-theory and examines their stability properties in various geometric settings.

Findings

Stability condition linked to Laplacian spectrum on (1,1)-forms.

CP(3) solutions satisfy the stability condition.

Instability arises in product spaces with continuous isometries.

Abstract

Eleven-dimensional supergravity admits non-supersymmetric solutions of the form AdS(5)xM(6) where M(6) is a positive Kahler-Einstein space. We show that the necessary and sufficient condition for such solutions to be stable against linearized bosonic supergravity perturbations can be expressed as a condition on the spectrum of the Laplacian acting on (1,1)-forms on M(6). For M(6)=CP(3), this condition is satisfied, although there are scalars saturating the Breitenlohner-Freedman bound. If M(6) is a product S(2)xM(4) (where M(4) is Kahler-Einstein) then there is an instability if M(4) has a continuous isometry. We show that a potential non-perturbative instability due to 5-brane nucleation does not occur. The bosonic Kaluza-Klein spectrum is determined in terms of eigenvalues of operators on M(6).