Supersymmetry breaking branes on solvmanifolds and de Sitter vacua in string theory

TL;DR

This work develops a ten-dimensional framework for de Sitter vacua in type IIA string theory on solvmanifolds with O6/D6 sources by introducing a non-pure polyform $X_-$ to model supersymmetry-breaking branes. The authors implement twist constructions on almost abelian solvmanifolds within generalized geometry, derive both supersymmetric and non-supersymmetric solutions, and show that a de Sitter solution arises for $ extGamma^2= frac{1}{2}$ with suitable fluxes and source embeddings. They further analyze the four-dimensional effective potential, identifying a de Sitter minimum in the volume and dilaton moduli and demonstrating consistency with both the modified and standard brane actions under specific parameter relations. The results provide a concrete geometric mechanism for uplifting to de Sitter within a conservative, geometric setting, with a detailed treatment of localization, warping, and potential non-geometric aspects of the background. Overall, the paper offers a novel route to incorporate SUSY-breaking branes in solvmanifold compactifications and reveals conditions under which stable de Sitter vacua can arise in ten dimensions and their four-dimensional effective descriptions.

Abstract

We consider IIA compactifications on solvmanifolds with O6/D6 branes and study the conditions for obtaining de Sitter vacua in ten dimensions. While this is a popular set-up for searching de Sitter vacua, we propose a new method to include supersymmetry breaking sources. For space-time filling branes preserving bulk supersymmetry, the energy density can easily be extremized with respect to all fields, thanks to the replacement of the DBI action by a pullback of a special form given by a pure spinor. For sources breaking bulk supersymmetry, we propose to replace the DBI action by the pullback of a more general polyform, which is no longer pure. This generalization provides corrections to the energy-momentum tensor which give a positive contribution to the cosmological constant. We find a de Sitter solution to all (bulk and world-volume) equations derived from this action. We argue it solves the equations derived from the standard source action. The paper also contains a review of solvmanifolds.

Figures (2)

• Figure 1: Mostow bundle for the solvmanifolds $\epsilon_2$ and $\epsilon_{1,1}$. The base is the circle in the $t$ direction, and due to the nilradical being abelian the fiber is $T^2$. The fibration is encoded in $\mu(t)$ which is either a rotation or a "hyperbolic rotation" twisting the $T^2$ moving along the base.
• Figure 2: Dependence of the potential on dilaton and volume modulus