A $dS_4$ maximum in M-theory from Casimir energies on Riemann-flat manifolds

Abstract

We describe a fully explicit, four-dimensional, top-down de Sitter saddle, constructed via compactification of M-theory on the Riemann-flat manifold $T^7/\mathbb{Z}_8$. The solution has a vacuum energy of $5.02\cdot 10^{-10}\,M_\text{Pl}^4$, a hierarchy $m_{KK}/H\sim 10^{2}$, and is under control with respect to higher-loop and higher-derivative corrections. While the solution is the first example of a top-down dS maximum in four dimensions, it is far from being phenomenologically viable. The solution also suggests several promising directions in the search for higher-quality dS saddles in the Riemann-flat Landscape, which we describe.