On new maximal supergravity and its BPS domain-walls

We revise the SU(3)-invariant sector of $\mathcal{N}=8$ supergravity with dyonic SO(8) gaugings. By using the embedding tensor formalism, analytic expressions for the scalar potential, superpotential(s) and fermion mass terms are obtained as a function of the electromagnetic phase $\omega$ and the scalars in the theory. Equipped with these results, we explore non-supersymmetric AdS critical points at $\omega \neq 0$ for which perturbative stability could not be analysed before. The $\omega$-dependent superpotential is then used to derive first-order flow equations and obtain new BPS domain-wall solutions at $\omega \neq 0$. We numerically look at steepest-descent paths motivated by the (conjectured) RG flows.