Exploring the landscape of (anti-) de Sitter and Minkowski solutions: group manifolds, stability and scale separation

Abstract

We classified in [1] certain 10d supergravity solutions with a 4d de Sitter, Minkowski or anti-de Sitter spacetime. We then found new solutions in previously unexplored classes. In this paper we study their properties, compare them to swampland conjectures, and make new observations.Using new numerical tools, we first identify all Lie algebras underlying the 6d group manifolds, allowing us to discuss their compactness. We then investigate scale separation, and prove related no-go theorems. Last but not least, we automatize and analyze the stability of all solutions. This leads us to propose the Massless Minkowski Conjecture, claiming the systematic presence of a 4d flat direction.

Automated consistent truncations and stability of flux compactifications

“…3.3], we know that adding more scalar fields, thus increasing the size of the mass matrix, can only lower its minimal eigenvalue. As a physics consequence, solutions are expected to be more unstable here than they were found to be in [5]. We also recall from Section 2.1 that the 4d theory used here is unlikely to be a low energy effective theory, but is rather a consistent truncation.…”

“…There are a few notable exceptions to the latter, the most impressive change being observed for m + 5577 1 going from η V ≈ −4.75 to η V ≈ −32.7. We note that this solution is on a non-compact group manifold [5]…”

“…6 We used | • | int to denote the contractions of the form only with respect to the internal metric G ab on the group manifold. For type IIA we have dualized a spacetime filling 5 Strictly speaking, T (p) I 10…”

“…Classifying these solutions and understanding their properties therefore drives a lot of activity. Related conjectures [1][2][3][4][5] have appeared in the context of the swampland program [6,7]. Of particular interest is the question of stability of these solutions: non-supersymmetric solutions with maximally symmetric spacetimes have been conjectured to be unstable: see e.g.…”

“…Those are candidates to be classical string backgrounds; if they turn out to be in the classical string regime, then the stability analysis provided here is sufficient. For these 10d solutions, we follow the ansatz and conventions of [15]: the 6d space is a group manifold (whose compactness is a priori not ensured, but analysed in detail in [5]), the fluxes have constant components in the left-invariant basis, and the only extended objects included are D p -branes and orientifold O p -planes. The latter are smeared, going together with a constant dilaton and no warp factor.…”