Classification and stability of vacua in maximal gauged supergravity

This article presents a systematic study of critical points for the SL(8, R)-type gauging in four dimensional maximal gauged supergravity. We determine all the possible vacua for which the origin of the moduli space becomes a critical point. We formulate a new tool which enables us to find analytically the mass spectrum of the corresponding vacua in terms of eigenvalues of the embedding tensor. When the cosmological constant is nonvanishing, it turns out that many vacua obtained by the dyonic embedding admit a single deformation parameter of the theory, in agreement with the results of the recent paper by Dall'Agata, Inverso and Trigiante [arXiv:1209.0760]. Nevertheless, it is shown that the resulting mass spectrum is independent of the deformation parameter and can be classified according to the unbroken gauge symmetry at the vacua, rather than the underlying gauging. We also show that the generic Minkowski vacua exhibit instability.