Fourteen new stationary points in the scalar potential of SO(8)-gauged $$ \mathcal{N} = 8 $$ , D = 4 supergravity

Abstract

Fourteen new stationary points in the scalar potential of SO (8) (8) is extended by fourteen new entries, whose properties have been obtained numerically using the sensitivity backpropagation technique. Eight of the new solutions break the gauge group completely, while three have a residual symmetry of U (1). Three further ones break the gauge group to U (1) × U (1). While the approximate numerical data are somewhat inconclusive, there is evidence that one of these may have a residual N = 1 supersymmetry, hence correspond to a stable vacuum. It must be pointed out that this list of new solutions most likely is not exhaustive.

Charting the landscape of $ \mathcal{N} = 4 $ flux compactifications

“…Indeed, the solutions 3 (s 1 ,s 2 ) are nonsupersymmetric and still stable with a higher vacuum energy, as can be read from (4.10). This again differs from the situation in the prototypical N = 8 supergravity with SO (8) gauging, where the vacuum that preserves all supersymmetry has the highest potential energy of all known critical points [47].…”

Properties of the new $$ \mathcal{N} $$ = 1 AdS4 vacuum of maximal supergravity

“…Between 2008 and 2010, there has been also a considerable progress in developing numerical techniques to search for the critical points in the full 70-parameter space. Those methods were used by one of us to explore the vacuum structure of maximal gauged supergravity theories in three dimensions [16,17] and then ported to four dimensions in [18][19][20]. In particular, a new N = 1 supersymmetric critical point S1200000 2 was discovered in [18] and, using the numerical data as a guide, subsequently confirmed analytically in [14].…”

Exceptional flux compactifications

“…However, one might also be interested in the interplay between gaugings, fluxes and moduli stabilisation: in short, fluxes were introduced in order to achieve moduli stabilisation. Sketchily, the picture in this respect seems to be the following Semisimple gaugings are likely to produce critical points and moduli stabilisation [49][50][51][52], but we will show that their embedding as type II flux compactifications involves highly non-geometric backgrounds. On the other hand, nilpotent gaugings can be obtained from type II compactifications including gauge fluxes [60], but they seem not to be enough to get moduli stabilisation.…”

“…Note that this critical point relies on the Breitenlohner-Freedman bound to be perturbatively stable. More recently, this classification has been extended with a number of critical points with smaller or trivial invariance groups, which have been obtained with a numerical procedure [49,50].…”