Supersymmetric de Sitter solutions in D=11 supergravity

Abstract

We determine the necessary and sufficient conditions for warped product dSⁿ solutions, n ≥ 5 to preserve supersymmetry in D = 11 supergravity. We prove that for n ≥ 7, all such solutions are flat, with vanishing 4-form. We also show that the only warped product dS⁶ solutions are either the maximally supersymmetric AdS₇ × S⁴ solution, or R_^1,6 × N₄ where N₄ is hyperKähler, with vanishing 4-form. We also fully classify all supersymmetric warped product dS⁵ solutions. The 6-dimensional internal space is shown to be a warped product S¹ ×_w S¹ ×_w M₄, where M₄ is conformal to a hyperKähler manifold. Furthermore, we prove that if the 4-form is parallel, then M₄ admits a hyperKähler potential.