Stability of AdS_p x M_q Compactifications Without Supersymmetry

TL;DR

This paper demonstrates that AdS_p x S^q compactifications without supersymmetry are generally stable against small fluctuations, providing insights into their holographic duals and stability conditions, especially for specific compactification geometries.

Contribution

It proves the classical stability of non-supersymmetric AdS_p x S^q vacua and analyzes stability conditions for various compact Einstein spaces, including the impact of a cosmological term.

Findings

AdS_p x S^q vacua are classically stable against small fluctuations.

Stability depends on the value of q, with q >= 9 being stable.

The specific AdS_4 x S^6 compactification with a cosmological term is unstable.

Abstract

We study the stability of Freund-Rubin compactifications, AdS_p x M_q, of p+q-dimensional gravity theories with a q-form field strength and no cosmological term. We show that the general AdS_p x S^q vacuum is classically stable against small fluctuations, in the sense that all modes satisfy the Breitenlohner-Freedman bound. In particular, the compactifications used in the recent discussion of the proposed bosonic M-theory are perturbatively stable. Our analysis treats all modes arising from the graviton and the q-form, and is completely independent of supersymmetry. From the masses of the linearized perturbations, we obtain the dimensions of some operators in possible holographic dual CFT's. Solutions with more general compact Einstein spaces need not be stable, and in particular AdS_p x S^n x S^{q-n} is unstable for q < 9 but is stable for q >= 9. We also study the AdS_4 x S^6 compactification of massive type IIA supergravity, which differs from the usual Freund-Rubin compactification in that there is a cosmological term already in ten dimensions. This nonsupersymmetric vacuum is unstable.