String theory has never produced a universe with positive dark energy. This is the single most embarrassing fact about the theory: the universe we observe has a small, positive cosmological constant — dark energy that drives accelerating expansion — and string theory cannot naturally explain it.
In 2025, Bento and Montero constructed the first explicit de Sitter solution from string theory using the Casimir effect in M-theory compactification. Extra dimensions curled into torus shapes generate a Casimir energy — a quantum vacuum effect from the boundary conditions the compact dimensions impose. The Casimir energy is positive, which means it acts like dark energy: it drives expansion.
The solution works. It is explicit, calculable, and derived from first principles. It is also wrong in two specific ways. First, it lives in five dimensions, not four. The dark energy emerges in a five-dimensional spacetime, and reducing to four dimensions is a separate problem that the construction does not solve. Second, the magnitude of the Casimir energy is 10⁻¹⁵ in natural units, while the observed dark energy is 10⁻¹²³. The calculation is off by 108 orders of magnitude.
Both problems are well-known to the authors and to the community. The paper is not claiming to solve dark energy. It is claiming something more modest and arguably more important: that string theory can produce positive vacuum energy at all. The prior state of affairs — where no explicit construction existed — was a genuine crisis for the theory. If string theory cannot produce a universe with positive dark energy even in principle, it cannot describe our universe. Bento and Montero show that it can, in principle. The 108 orders of magnitude and the wrong number of dimensions are engineering problems, not conceptual ones.
Whether this is progress depends on what you count as the hard part. If the hard part is showing that positive vacuum energy is compatible with string theory, then this is significant progress — the first demonstration in decades of work. If the hard part is matching the observed value, then the gap is almost comically large, and the demonstration that the sign is right is a small step in a long journey.
The geometric simplicity of the construction is notable. Tori — the shapes of the extra dimensions — are the simplest compact manifolds. The Casimir effect on a torus is a standard calculation. The reason this hadn't been done before is not mathematical difficulty but a set of assumptions about which compactifications were physically relevant. The field had focused on Calabi-Yau manifolds, which are geometrically complex and produce negative or zero vacuum energy. The torus was overlooked not because it was wrong but because it was too simple for a community that expected the answer to be complicated.