DeWolfe, Oliver and Freedman, Daniel Z. and Gubser, Steven S. and Horowitz, Gary T. and Mitra, Indrajit (2002) Stability of AdSp×Mq compactifications without supersymmetry. Physical Review D, 65 (6). Art. No. 064033. ISSN 0556-2821. http://resolver.caltech.edu/CaltechAUTHORS:DEWprd02a
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We study the stability of Freund-Rubin compactifications, AdSp×Mq, of (p+q)-dimensional gravity theories with a q-form field strength and no cosmological term. We show that the general AdSp×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 AdSp×S^n×S^(q-n) is unstable for q<9 but is stable for q>~9. We also study the AdS4×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.
|Additional Information:||©2002 The American Physical Society Received 22 September 2001; published 4 March 2002 We would like to thank O. Bergman, I. Klebanov, and E. Witten for useful discussions. We are particularly grateful to A. Brandhuber for help checking some of the equations in the massive type IIA compactifications. The work of S.S.G. and I.M. was supported in part by the DOE under grant DEFG03-92ER40701 and through the Outstanding Junior Investigator program. I.M. was also supported under grant DEFG02-91ER40671. The work of O.D. was supported by the NSF under grant PHY-99-07949. The work of G.H. was supported by the NSF under grant PHY-00-70895. The work of D.Z.F. was supported by the NSF under grant PHY-97-22072. I.M. thanks the Institute for Theoretical Physics, Santa Barbara and the Particle Theory Group at Caltech for their hospitality during most of the phases of this project.|
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