TY - JOUR

T1 - Stability of AdS p×M q compactifications without supersymmetry

AU - DeWolfe, Oliver

AU - Freedman, Daniel Z.

AU - Gubser, Steven S.

AU - Horowitz, Gary T.

AU - Mitra, Indrajit

N1 - Copyright:
Copyright 2011 Elsevier B.V., All rights reserved.

PY - 2002

Y1 - 2002

N2 - We study the stability of Freund-Rubin compactifications, AdS p×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×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×S n×S q-n is unstable for q<9 but is stable for q≥9. We also study the AdS 4×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.

AB - We study the stability of Freund-Rubin compactifications, AdS p×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×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×S n×S q-n is unstable for q<9 but is stable for q≥9. We also study the AdS 4×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.

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U2 - 10.1103/PhysRevD.65.064033

DO - 10.1103/PhysRevD.65.064033

M3 - Article

AN - SCOPUS:0037087898

VL - 65

JO - Physical review D: Particles and fields

JF - Physical review D: Particles and fields

SN - 1550-7998

IS - 6

M1 - 064033

ER -