The criterion for vacuum stability in Kaluza-Klein supergravity |
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Authors: | MJ Duff BEW Nilsson CN Pope |
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Institution: | Blackett Laboratory, Imperial College, London SW7 2BZ, UK |
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Abstract: | We prove that in the spectrum of the d = 4 theory obtained by Freund-Rubin compactification of d = 11 superconductivity, only fields of spin 0+ can give rise to classical instabilities. The criterion for stability in the 0+ sector can be expressed as a certain lower bound on the Lichnerowicz operator ΔL on the d = 7 compact space. Thus not only are supersymmetric vacua always stable but so are the corresponding non-supersymmetric vacua obtained by reversing the orientation of the compact space, since the 0+ spectrum is insensitive to the orientation. Examples are the orientation-reversed spaces with N = 0 obtained from the squashed seven-sphere with N = 1 and from SU(3) ×SU(2) ×U(1) spaces with N = 2 supersymmetry. Product spaces, on the other hand, are always unstable. Finally, we examine the massless sectors of the squashed seven-sphere vacua, and find an additional 135 massless scalars. |
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