Supersymmetric dS n solutions for n ⩾ 5in D = 11 supergravity

Source abstract

Abstract We determine the necessary and sufficient conditions for warped product dS n solutions, 5 ⩽ n ⩽ 10, to preserve supersymmetry in D = 11 supergravity, without assuming factorization of the Killing spinors. We prove that for 7 ⩽ n ⩽ 10, all such solutions are flat, with vanishing four-form. We also show that the only warped product dS 6 solutions are either the maximally supersymmetric AdS 7 × S 4 solution, or R 1 , 6 × N 4 where N 4 is hyperKähler, with vanishing four-form. Supersymmetric warped product dS 5 solutions are then classified; it is shown that all such solutions are generalized M5-brane configurations, for which the transverse space is R × N 4 , and N 4 is a hyperKähler manifold. If the four-form is covariantly constant, then N 4 admits a hyperKähler potential.