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Tachyonic Kaluza-Klein modes and the AdS swampland conjecture. (English) Zbl 1454.83119

Summary: We compute the Kaluza-Klein spectrum of the non-supersymmetric \( \mathrm{SO}(3) \times \mathrm{SO}(3) \)-invariant \( \mathrm{AdS}_4\) vacuum of 11-dimensional supergravity, whose lowest-lying Kaluza-Klein modes belong to a consistent truncation to 4-dimensional \(\mathcal{N} = 8\) supergravity and are stable. We show that, nonetheless, the higher Kaluza-Klein modes become tachyonic so that this non-supersymmetric \( \mathrm{AdS}_4\) vacuum is perturbatively unstable within 11-dimensional 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 \( \mathrm{AdS}_4\) vacua.

MSC:

83E15 Kaluza-Klein and other higher-dimensional theories
83E50 Supergravity
81T60 Supersymmetric field theories in quantum mechanics
81R40 Symmetry breaking in quantum theory

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