[Paper Review] A new light on the darkest corner of the landscape

Johan Blåbäck, Ulf Danielsson+1 more|arXiv (Cornell University)|Oct 26, 2018

Black Holes and Theoretical Physics45 references22 citations

TL;DR

This paper presents a metastable de Sitter vacuum in 4D $σ$-model compactifications of massive type IIA string theory on $\mathbb{T}^6/(\mathbb{Z}_2 \times \mathbb{Z}_2)$, stabilized by O6 planes and KK monopoles. By relaxing the Jacobi constraint on metric fluxes, the authors eliminate tachyonic instabilities, yielding a single flat axionic direction; this solution violates the refined de Sitter swampland conjecture, challenging its universality.

ABSTRACT

Motivated by the recently proposed bounds on the slow-roll parameters for scalar potentials arising from string/M-theory compactifications, a.k.a. the Refined de Sitter Swampland conjecture, we explore the sharpness of such constraints within 4D supergravities coming from compactifications of massive type IIA string theory on $\mathbb{T}^{6}/(\mathbb{Z}_{2}\, imes\,\mathbb{Z}_{2})$. With the aid of a numerical technique, known as differential evolution, we are able to find a de Sitter extremum which is fully metastable up to one single flat direction. This solution is supported by spacetime filling sources such as O6 planes and KK monopoles. Our example violates the bound imposed by this conjecture.

Motivation & Objective

• To test the validity of the refined de Sitter swampland conjecture in controlled 4D supergravity models derived from string compactifications.
• To investigate whether metastable de Sitter vacua can be realized in massive type IIA compactifications with geometric fluxes and spacetime-filling sources.
• To explore the role of KK monopoles in stabilizing the scalar potential and removing tachyonic modes.
• To determine whether the presence of a flat axionic direction—universal in superpotentials linear in multiple moduli—can coexist with full metastability in dS vacua.

Proposed method

• The authors employ a numerical optimization technique, differential evolution, to search for critical points in the scalar potential of an $σ$-model derived from massive type IIA compactification on $\mathbb{T}^6/(\mathbb{Z}_2 \times \mathbb{Z}_2)$.
• They relax the Jacobi constraint on metric fluxes, allowing for the inclusion of spacetime-filling KK monopoles, which are geometrically interpreted as torsion forms in $\mathrm{SU}(3)$-structured compactifications.
• The scalar potential is computed from flux-parameters and moduli, with the superpotential assumed to be linear in the $S$ and $T_i$ moduli, ensuring a universal flat axionic direction.
• The mass spectrum is computed via the Hessian of the potential, normalized by the vacuum energy, with eigenvalues evaluated at the critical point to assess stability.
• The solution is verified numerically by plotting the potential along eigenvectors of the Hessian, confirming a single zero eigenvalue and all others positive.
• The flux parameters are explicitly tabulated, and the solution is checked for consistency with the supergravity constraints and moduli space geometry.

Experimental results

Research questions

• RQ1 Can a fully metastable de Sitter vacuum be constructed in massive type IIA compactifications using only geometric fluxes and spacetime-filling sources?
• RQ2 Does the inclusion of KK monopoles—via relaxation of the Jacobi constraint—enable the removal of tachyonic instabilities while preserving a flat axionic direction?
• RQ3 Is the refined de Sitter swampland conjecture violated by a concrete, numerically constructed solution in a controlled supergravity framework?
• RQ4 What is the role of the universal flat axionic direction in models with superpotentials linear in multiple moduli, and can it be stabilized without introducing non-geometric fluxes?
• RQ5 Can the interplay between fluxes, O6 planes, and KK monopoles generate a stable dS vacuum without relying on non-perturbative or non-geometric effects?

Key findings

• The authors construct a de Sitter vacuum that is fully metastable except for one flat axionic direction, with all other scalar modes having positive squared masses.
• The flat direction arises universally in models with superpotentials linear in multiple moduli, specifically a combination of the axions of $S$ and $T_i$ moduli.
• The tachyonic instability present in earlier solutions is removed by introducing KK monopoles through relaxation of the Jacobi constraint on metric fluxes.
• The smallest non-zero eigenvalue of the Hessian is $0.00383681$, indicating a very shallow but positive mass, while the lightest mode is exactly zero, corresponding to the flat axionic direction.
• The solution violates the refined de Sitter swampland conjecture, as the first slow-roll parameter is not bounded below by $\mathcal{O}(1)$, and the potential exhibits a flat direction.
• The flux parameters are explicitly tabulated, and the mass spectrum is computed with high numerical precision, confirming the stability of the solution except for the flat direction.