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

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.

57 pages, 3 figures. Important additions (concerning the validity of our solution in string theory); version to appear in JHEP

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• Open problems on classical de Sitter solutions
• Lattices, cohomology and models of six dimensional almost abelian solvmanifolds
• On the geometry underlying supersymmetric flux vacua with intermediate SU(2) structure
• O(d,d)-Duality in String Theory
• Revisiting constraints on uplifts to de Sitter vacua
• De Sitter Vacua from a D-term Generated Racetrack Uplift
• Formality and symplectic structures of almost abelian solvmanifolds