4D de Sitter from string theory via 6D supergravity

We propose a new way to obtain explicit de Sitter (dS) solutions from controlled string-theory constructions. The Dine-Seiberg problem is usually interpreted as meaning that weak-coupling expansions generically drive runaways rather than allowing stabilized maximally symmetric spacetimes. Using the special case of string compactifications to 6D we confirm that this argument does prevent the existence of classical maximally symmetric 6D solutions but argue that it allows time-independent classical solutions with maximal 4D symmetry, including dS solutions. We review how minimal gauged chiral 6D supergravity evades standard dS no-go theorems by having a positive scalar potential and describe the known 4D classical dS, AdS and Minkowski solutions. The stringy provenance of this 6D supergravity was obscure until Grimm and collaborators found it to be produced by direct F-theory Calabi-Yau flux compactifications. We construct classical 4D maximally symmetric solutions for this 6D supergravity and provide explicit solutions of the higher-dimensional field equations corresponding to dS, AdS and flat spacetimes in 4D, allowing interesting hierarchies of scales. We show how the singularities of these solutions are consistent with the back-reaction of two space-filling 4D brane-like sources situated within the extra dimensions and infer some of the properties of these sources using the formalism of point particle effective field theory (PPEFT). These tools relate the near-source asymptotic forms of bulk fields to source properties and have been extensively tested for more prosaic physical systems involving the back-reaction of small sources, such as the dependence of atomic energy levels on nuclear properties. We use it to determine the tension of the brane-like sources (that can be positive) and its derivatives. We verify that the solutions are in the weak coupling/large volume regime required to neglect quantum and α′ effects.