Assess validity of approximations near codimension-two singularities

Determine whether the perturbative expansion parameters (such as string coupling, inverse compactification volume, and higher-derivative corrections) remain small near the codimension-two singularities of the 6D gauged chiral supergravity solutions that yield four-dimensional de Sitter space, so that the low-energy supergravity approximation remains under control in those regions.

Background

The construction produces 4D de Sitter solutions in six-dimensional gauged supergravity with back-reacting codimension-two sources, leading to localized singularities. Reliability of the solutions requires that small expansion parameters remain small everywhere, including near singularities, otherwise higher-order or stringy corrections could invalidate the classical approximations.

The authors explicitly note that this issue remains unresolved and is central to establishing the trustworthiness of the proposed de Sitter backgrounds.