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The landscape of possible four-dimensional low-energy effective theoriesarising from compactifications of string/M-theory seems vast. This might leadone to believe that any consistent-looking effective field theory coupled togravity can be obtained as a low-energy limit of string theory. However, a setof "swampland" conjectures suggests that this is not true and that, in fact,there is an even larger set of effective field theories that cannot be obtainedin this way. In particular, the AdS instability swampland conjecture assertsthat nonsupersymmetric anti-de Sitter vacua are unstable. These swamplandcriteria can have implications for, for instance, low-energy physics andcosmology.  M-theory is a nonperturbative unification of all superstring theories. Itslow-energy limit, eleven-dimensional supergravity, admits two compactificationson the squashed seven-sphere. One of the solutions has one unbrokensupersymmetry ($\mathcal{N} = 1$) while the other has none ($\mathcal{N} = 0$).Due to the AdS instability swampland conjecture, the latter should be unstable.However, this has not been demonstrated explicitly. To study the stability ofthe $\mathcal{N} = 0$ vacuum, we investigate the mass spectrum of the theory.The main advancement compared to previous attempts is the realisation that allmass operators in the Freund-Rubin compactification are related to a universalLaplacian, allowing us to relate Weyl tensor terms to group invariants. Onelimitation of the group-theoretical method we employ is that it can lead tofalse roots. This is remedied, at least in part, by demanding that the fieldsform supermultiplets in the $\mathcal{N} = 1$ case. Although we arrive at aneigenvalue spectrum for all operators of interest, there is a hint that theresults may be incomplete. Thus, we do not reach a decisive conclusionregarding the investigated type of instability.

Compactifications of String/M-Theory and the Swampland: A Study of the  AdS$_\text{4}$ Mass Spectrum of Eleven-Dimensional Supergravity on the  Squashed Seven-Sphere