Towards an explicit construction of de Sitter solutions in classical supergravity

We revisit the stringy construction of four-dimensional de-Sitter solutions using orientifolds O8_±, proposed by Córdova et al. (2019) [1]. While the original analysis of the supergravity equations is largely numerical, we obtain semi-analytic solutions by treating the curvature as a perturbative parameter. At each order we verify that the (permissive) boundary conditions at the orientifolds are satisfied. To illustrate the advantage of our result, we calculate the four-dimensional Newton constant as a function of the cosmological constant. We also discuss how the discontinuities at O8₋ can be accounted for in terms of corrections to the worldvolume action.