Tachyonic Kaluza-Klein modes and the AdS swampland conjecture
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Springer
Received: May 28, 2020 Accepted: July 25, 2020 Published: August 28, 2020
Emanuel Malek,a Hermann Nicolaia and Henning Samtlebenb a
Max-Planck-Institut f¨ ur Gravitationsphysik (Albert-Einstein-Institut), Am M¨ uhlenberg 1, 14476 Potsdam, Germany b Univ Lyon, Ens de Lyon, Univ Claude Bernard, CNRS, Laboratoire de Physique, F-69342 Lyon, France
E-mail: [email protected], [email protected], [email protected] Abstract: We compute the Kaluza-Klein spectrum of the non-supersymmetric SO(3) × SO(3)-invariant AdS4 vacuum of 11-dimensional supergravity, whose lowest-lying KaluzaKlein modes belong to a consistent truncation to 4-dimensional N = 8 supergravity and are stable. We show that, nonetheless, the higher Kaluza-Klein modes become tachyonic so that this non-supersymmetric AdS4 vacuum is perturbatively unstable within 11dimensional supergravity. This represents the first example of unstable higher Kaluza-Klein modes and provides further evidence for the AdS swampland conjecture, which states that there are no stable non-supersymmetric AdS vacua within string theory. We also find 27 infinitesimal moduli amongst the Kaluza-Klein modes, which hints at the existence of a family of non-supersymmetric AdS4 vacua. Keywords: Flux compactifications, Supergravity Models, Superstring Vacua, Supersymmetry Breaking ArXiv ePrint: 2005.07713
c The Authors. Open Access, Article funded by SCOAP3 .
https://doi.org/10.1007/JHEP08(2020)159
JHEP08(2020)159
Tachyonic Kaluza-Klein modes and the AdS swampland conjecture
Contents 1
2 Kaluza-Klein spectroscopy 2.1 SU(8) mass matrix
2 5
3 The SO(3) × SO(3)-invariant AdS4 vacuum
6
4 Scalar harmonics
9
5 The Kaluza-Klein spectrum
10
6 Conclusions
16
A SU(8) vs. SL(8,R) bases
17
1
Introduction
The stability of anti-de Sitter (AdS) spacetimes has been a long-standing question in theoretical physics. The question is particularly interesting in the case of non-supersymmetric AdS spacetimes, which are not protected by supersymmetry arguments and corresponding positive mass theorems [1]. In the context of string theory, the fate of non-supersymmetric AdS vacua is especially important. For example, non-supersymmetric AdS vacua provide one of the most explicit ways to apply the AdS/CFT correspondence to QCD or condensed matter systems [2]. Moreover, non-supersymmetric AdS compactifications provide a simpler class of non-supersymmetric string solutions than de Sitter vacua, which are time-dependent. Therefore, non-supersymmetric AdS solutions can be seen as a natural stepping stone to understanding de Sitter vacua in string theory. However, so far no fully-fledged examples of non-supersymmetric but stable AdS vacua in string theory have been constructed. One of the most efficient ways of constructing nonsupersymmetric AdS vacua in string theory is by uplifting non-supersymmetric solutions of lower-dimensional gauged supergravities. While many such AdS solutions are known, for example in N = 8 supergravities in four [3–10] and five dimensions [11
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