2026

1. A \(dS_4\) maximum in M-theory from Casimir energies on Riemann-flat manifolds

   Miquel Aparici, Bruno Valeixo Bento, and Miguel Montero

   Sep 2026

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   We describe a fully explicit, four-dimensional, top-down de Sitter saddle, constructed via compactification of M-theory on the Riemann-flat manifold \(T^7/ℤ_8\). The solution has a vacuum energy of \(5.02⋅10^{−10} M^4_{\rm Pl}\), a hierarchy \(m_{\rm KK}/H∼10^2\), 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.

2. CasimirRFM: A Mathematica package for Riemann-flat compactifications with Casimir energies

   Bruno Valeixo Bento

   Jul 2026

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   CasimirRFM is a Mathematica package for the study of compactifications on Riemann-flat manifolds and the computation of one-loop Casimir energies in higherdimensional field theories and supergravity. It implements an efficient numerical evaluation of lattice sums using Ewald summation, and computes both lower-dimensional Casimir potentials and local higher-dimensional Casimir energy densities, allowing for general massless spectra and twisted boundary conditions. The package provides tools for constructing and analysing the finite groups defining these manifolds, determining invariant metrics and cohomology bases, identifying compatible spin structures, and computing moduli-space metrics. Moreover, it evaluates the traces of holonomy elements in the graviton, p-form, spinor, and Rarita-Schwinger representations. We describe the mathematical formulation and numerical implementation of the package, and illustrate its use through a compactification of Type IIB supergravity on \(T^6/ℤ_8\), including the computation of the Casimir potential and the visualization of localised Casimir-brane contributions.

2025

1. Constraining strongly-warped extra dimensions with rotating black holes

   Bruno Valeixo Bento, and Miquel Salicrú Herberg

   Nov 2025

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   Massive bosonic fields can trigger superradiant instabilities in rotating astrophysical black holes leading to gaps in their mass-spin distribution. For spin-2 fields, the instability timescale is orders of magnitude shorter than for any other superradiant mode, thereby yielding much stronger constraints. We consider a tower of ultra-light spin-2 fields arising from a warped compactification of a single extra dimension and translate superradiant constraints on their masses into constraints on the warping. As a concrete scenario we consider the 2-brane Randall-Sundrum model and find constraints on the size of the extra dimension and the curvature of AdS5. We discuss the implications of these bounds for strongly warped throats and D-brane uplifts commonly used in attempts to realise metastable de Sitter vacua in string theory.

2. de Sitter no-go’s for Riemann-flat manifolds and a link to semidefinite optimisation

   Bruno Valeixo Bento, and Miguel Montero

   Oct 2025

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   We establish a no-go theorem in the context of string and M-theory flux compactifications on Riemann-Flat manifolds with Casimir energy. Specifically, we show that no dS minimum exists in this setup in dimension d>3. The case of dS3 minima is not excluded, but their actual fate can only be ascertained via an explicit construction. We also point out that the problem of finding dS minima on RFM’s and more general flux compactifications is mathematically equivalent to a semidefinite programming problem, identical to those studied in CFT bootstrap, and hence the search for dS can benefit from the existing vast literature and numerical tools. We illustrate this in a toy model.

3. An M-theory dS maximum from Casimir energies on Riemann-flat manifolds

   Bruno Valeixo Bento, and Miguel Montero

   Jul 2025

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   We initiate the study of flux compactifications on non-supersymmetric Riemann-flat manifolds (RFM’s) with Casimir energy. While curvature and other corrections are suppressed in RFM’s, the inclusion of Casimir energies allows one to evade standard dS no-go theorems, and the absence of orientifolds or other singular sources means that the construction is completely captured by ten or eleven-dimensional supergravity. We obtain a fully explicit formula for the Casimir stress-energy in a general RFM, including its ten or eleven-dimensional profile. The Casimir energy localizes in particular loci of the RFM, which we call “Casimir branes”. The tension of Casimir branes sometimes cancels exactly, due to a spacetime analog of worldsheet Atkin-Lehner symmetry. We use Casimir energies to construct an explicit dS5 maximum solution of a flux compactification of M-theory on a specific 6-dimensional RFM.

4. EFT & Species Scale: Friends or foes?

   Bruno Valeixo Bento, and João F. Melo

   Jan 2025

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   Recently the notion that quantum gravity effects could manifest at scales much lower than the Planck scale has seen an intense Swamplandish revival. Dozens of works have explored how the so-called species scale – at which an effective description of gravity must break down – relates to String Theory and the Swampland conjectures. In particular, the interplay between this scale and the abundant towers of states becoming lighter in asymptotic regions of moduli spaces has proved to be key in understanding the real scale of quantum gravity. Nevertheless concerns have been raised regarding the validity of using infinite towers of states when estimating this scale within Effective Field Theory and, more precisely, the consistency of cutting the tower part way through in a framework that relies on a clear separation of scales. In this work we take an EFT point-of-view and provide a detailed perturbative derivation of the species scale – by computing the 1-loop graviton propagator in the presence of many fields – thereby clarifying common sources of confusion in the literature. Not only do we clarify the setup, assumptions and regimes of validity of the result, but more importantly apply the same methods to an infinite tower of states. We show how each state in the tower contributes to the species scale and how the procedure of counting only ”light fields” can be compatible with not cutting the tower, thereby maintaining the harmony between infinite towers and EFTs even in the context of the species scale.